query: what is the next number in the sequence 1 11 21 osrs

pos: Look-and-say sequence puzzle "What is the next number in the sequence 1, 11, 21, 1211, 111221?" is sometimes referred to as the Cuckoo's Egg, from a description of Morris in Clifford Stoll's book "The Cuckoo's Egg". There are many possible variations on the rule used to generate the look-and-say sequence. For example, to form the "pea pattern" one reads the previous term and counts all instances of each digit, listed in order of their first appearance, not just those occurring in a consecutive block. Thus, beginning with the seed 1, the pea pattern proceeds 1, 11 ("one 1"), 21 ("two 1s"), 1211

pos: Robert Morris (cryptographer) was involved in the production of the Rainbow Series of computer security standards, and retired from the NSA in 1994. He once told a reporter that, while at the NSA, he helped the FBI decode encrypted evidence. There is a description of Morris in Clifford Stoll's book "The Cuckoo's Egg". Many readers of Stoll's book remember Morris for giving Stoll a challenging mathematical puzzle (originally due to John H. Conway) in the course of their discussions on computer security: "What is the next number in the sequence 1 11 21 1211 111221?" (known as the look-and-say sequence). Stoll chose not

neg: Old School RuneScape In the article, Jagex explained the goals of the poll, and what each number bracket would unlock for the player community. In two weeks, it received enough votes for the game to be released. "OSRS" was released for Microsoft Windows, OS X, and Linux on 22 February 2013. Upon release, the game was only playable for accounts that had a membership subscription. The option for non-members to play in the limited free-to-play areas was granted in February 2015. Although "OSRS" has a small team of developers relative to that of the live version of "RuneScape", it receives regular patches and

neg: Sequence but 1 and themselves. Taking these in their natural order gives the sequence (2, 3, 5, 7, 11, 13, 17, ...). The prime numbers are widely used in mathematics and specifically in number theory. The Fibonacci numbers are the integer sequence whose elements are the sum of the previous two elements. The first two elements are either 0 and 1 or 1 and 1 so that the sequence is (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...). For a large list of examples of integer sequences, see On-Line Encyclopedia of Integer Sequences. Other examples of sequences include

neg: Highly totient number Highly totient number A highly totient number "k" is an integer that has more solutions to the equation φ("x") = "k", where φ is Euler's totient function, than any integer below it. The first few highly totient numbers are 1, 2, 4, 8, 12, 24, 48, 72, 144, 240, 432, 480, 576, 720, 1152, 1440 , with 1, 3, 4, 5, 6, 10, 11, 17, 21, 31, 34, 37, 38, 49, 54, and 72 totient solutions respectively. The sequence of highly totient numbers is a subset of the sequence of smallest number "k" with exactly "n" solutions to φ("x") =

neg: In-place matrix transposition course of several decades. For example, consider the 2×4 matrix: In row-major format, this would be stored in computer memory as the sequence (11, 12, 13, 14, 21, 22, 23, 24), i.e. the two rows stored consecutively. If we transpose this, we obtain the 4×2 matrix: which is stored in computer memory as the sequence (11, 21, 12, 22, 13, 23, 14, 24). If we number the storage locations 0 to 7, from left to right, then this permutation consists of four cycles: That is, the value in position 0 goes to position 0 (a cycle of length 1, no

neg: Van der Corput sequence der Corput sequence is For example, to get the decimal van der Corput sequence, we start by dividing the numbers 1 to 9 in tenths ("x"/10), then we change the denominator to 100 to begin dividing in hundredths ("x"/100). In terms of numerator, we begin with all two-digit numbers from 10 to 99, but in backwards order of digits. Consequently, we will get the numerators grouped by the end digit. Firstly, all two-digit numerators that end with 1, so the next numerators are 01, 11, 21, 31, 41, 51, 61, 71, 81, 91. Then the numerators ending with 2, so

neg: The Genius: Rule Breaker over a series of 10-minute round. In each round, players switch seats with each other with mutual consent. The objective is to have "exactly" five players with consecutive numbers seated next to each other. The sequence can include the players on both ends of the number range (e.g. 9-10-11-1-2), but cannot involve the X in any way, nor can it have more than five players. At the end of the round, the group is told the longest chain of consecutive numbers. The next round then begins, with each player's number increasing by 1. The player who was 11 in the

neg: Divisibility rule not comfortable with negative numbers, then use this sequence. (1, 10, 9, 12, 3, 4) Multiply the right most digit of the number with the left most number in the sequence shown above and the second right most digit to the second left most digit of the number in the sequence. The cycle goes on. Example: What is the remainder when 321 is divided by 13? Using the first sequence, <br> Ans: 1 × 1 + 2 × −3 + 3 × −4 = −17 Remainder = −17 mod 13 = 9 Example: What is the remainder when 1234567 is

neg: Hilbert number Hilbert number In number theory, a branch of mathematics, a Hilbert number is a positive integer of the form (). The Hilbert numbers were named after David Hilbert. The sequence of Hilbert numbers begins 1, 5, 9, 13, 17, ... ). A Hilbert prime is a Hilbert number that is not divisible by a smaller Hilbert number (other than 1). The sequence of Hilbert primes begins A Hilbert prime is not necessarily a prime number; for example, 21 is a composite number since . However, 21 a Hilbert prime since neither 3 nor 7 (the only factors of 21 other

neg: Arithmetic coding which is wasteful: one of the bit variations is never used. That is to say, A=00, B=01, and C=10, but 11 is unused. A more efficient solution is to represent a sequence of these three symbols as a rational number in base 3 where each digit represents a symbol. For example, the sequence "ABBCAB" could become 0.011201, in arithmetic coding as a value in the interval 0, 1). The next step is to encode this ternary number using a fixed-point binary number of sufficient precision to recover it, such as 0.0010110010 — this is only 10 bits; 2 bits are

neg: Hyperoperation as Graham's number and TREE(3). This recursion rule is common to many variants of hyperoperations (see below in definition). The "hyperoperation sequence" formula_4 is the sequence of binary operations formula_5, defined recursively as follows: For "n" = 0, 1, 2, 3, this definition reproduces the basic arithmetic operations of successor (which is a unary operation), addition, multiplication, and exponentiation, respectively, as So what will be the next operation after exponentiation? We defined multiplication so that formula_8, and defined exponentiation so that formula_9 so it seems logical to define the next operation, tetration, so that formula_10 with a tower of three

neg: Elementary cellular automaton it makes sense to interpret state at each time, "t", as an integer expressed in binary, producing a sequence "a"("t") of integers. In many cases these sequences have simple, closed form expressions or have a generating function with a simple form. The following rules are notable: The sequence generated is 1, 3, 5, 11, 21, 43, 85, 171, ... . This is the sequence of Jacobsthal numbers and has generating function It has the closed form expression Note that rule 156 generates the same sequence. The sequence generated is 1, 5, 21, 85, 341, 1365, 5461, 21845, ... . This

neg: Lateralus (song) It starts from 1, the next number is 1, and the next number being 2, creates the 2+1 which is 3, continuing in this mathematical progression. That’s how they found the chord progression. It began linking up to the Fibonacci sequence." The syllables Maynard sings in the first verse follow the first six numbers in the pattern, ascending and descending in the sequence 1-1-2-3-5-8-5-3. "Black (1), then (1), white are (2), all I see (3), in my infancy (5). Red and yellow then came to be (8), reaching out to me (5). Lets me see (3)." In the next verse,

neg:
Divisibility rule magnitude sequence
 (1, 3, 2, 6, 4, 5, cycle repeats for the next six digits) Period: 6 digits. Recurring numbers: 1, 3, 2, 6, 4, 5
Positive sequence Multiply the right most digit by the left most digit in the sequence and multiply the second right most digit by the second left most digit in the sequence and so on and so for. Next, compute the sum of all the values and take the modulus of 7.
Example: What is the remainder when 1036125837 is divided by 7?

Multiplication of the rightmost digit = 1 × 7 =

neg: Alternating bit protocol and a one-bit sequence number, i.e., a value that is 0 or 1. B has two acknowledge codes that it can send to A: ACK0 and ACK1. When A sends a message, it resends it continuously, with the same sequence number, until it receives an acknowledgment from B that contains the same sequence number. When that happens, A complements (flips) the sequence number and starts transmitting the next message. When B receives a message that is not corrupted and has sequence number 0, it starts sending ACK0 and keeps doing so until it receives a valid message with number 1.

neg: Fibonacci number of the "n"th month, the number of pairs of rabbits is equal to the number of new pairs (that is, the number of pairs in month "n" − 2) plus the number of pairs alive last month (that is, "n" − 1). This is the "n"th Fibonacci number. The name "Fibonacci sequence" was first used by the 19th-century number theorist Édouard Lucas. The first 21 Fibonacci numbers "F" for "n" = 0, 1, 2, ..., 20 are: The sequence can also be extended to negative index "n" using the re-arranged recurrence relation Thus the bidirectional sequence is The Fibonacci numbers

neg: Old School RuneScape Awards 2018. Old School RuneScape Old School RuneScape (OSRS) is a massively multiplayer online role-playing game (MMORPG) developed and published by Jagex. The game was first released in February 2013. "OSRS" was originally an exact copy of "RuneScape" as it was in August 2007, but has since received engine improvements, new content, and quality of life patches. Despite having a smaller staff and a slower relative update schedule, "OSRS" had more than twice the active players that "RuneScape" had by 2017. A mobile version of the game for Android and iOS was released in October 2018. The input mechanics are

neg: Old School RuneScape Old School RuneScape Old School RuneScape (OSRS) is a massively multiplayer online role-playing game (MMORPG) developed and published by Jagex. The game was first released in February 2013. "OSRS" was originally an exact copy of "RuneScape" as it was in August 2007, but has since received engine improvements, new content, and quality of life patches. Despite having a smaller staff and a slower relative update schedule, "OSRS" had more than twice the active players that "RuneScape" had by 2017. A mobile version of the game for Android and iOS was released in October 2018. The input mechanics are mainly point-and-click.

neg: Cyclic number the period is 1; for ternary it is 2, and so on. In binary, the sequence of cyclic numbers begins: In ternary: In quaternary: In quinary: In senary: In base 7: In octal: In nonary: In base 11: In duodecimal: In base 13: In base 14: In base 15: In hexadecimal: In base 17: In base 18: In base 19: In base 20: In base 21: In base 22: In base 23: In base 24: In base 25: Note that in ternary ("b" = 3), the case "p" = 2 yields 1 as a cyclic number. While single digits may

neg: Sliding window protocol As typically implemented, "n" is the next packet to be transmitted, i.e. the sequence number of the first packet not yet transmitted. Likewise, "n" is the first packet not yet received. Both numbers are monotonically increasing with time; they only ever increase. The receiver may also keep track of the highest sequence number yet received; the variable "n" is one more than the sequence number of the highest sequence number received. For simple receivers that only accept packets in order ("w" = 1), this is the same as "n", but can be greater if "w" > 1. Note the distinction:

neg: Collatz conjecture sequence in base two. The starting number 7 is written in base two as 111. The resulting Hailstone sequence is: For this section, consider the Collatz function in the slightly modified form This can be done because when "n" is odd, 3"n" + 1 is always even. If P(…) is the parity of a number, that is P(2"n") = 0 and P(2"n" + 1) = 1, then we can define the Hailstone parity sequence (or parity vector) for a number "n" as "p" = P("a"), where "a" = "n", and "a" = "f"("a"). What operation is performed (3"n" + 1)/2

neg: Rudin–Shapiro sequence Rudin–Shapiro sequence In mathematics, the Rudin–Shapiro sequence, also known as the Golay–Rudin–Shapiro sequence, is an infinite automatic sequence named after Marcel Golay, Walter Rudin, and Harold S. Shapiro, who independently investigated its properties. Each term of the Rudin–Shapiro sequence is either +1 or −1. The "n" term of the sequence, "b", is defined by the rules: where formula_3 are the digits in the binary expansion of "n". Thus "a" counts the number of (possibly overlapping) occurrences of the sub-string 11 in the binary expansion of "n", and "b" is +1 if "a" is even and −1 if "a" is odd.

neg: Jacobsthal number Jacobsthal number In mathematics, the Jacobsthal numbers are an integer sequence named after the German mathematician Ernst Jacobsthal. Like the related Fibonacci numbers, they are a specific type of Lucas sequence formula_1 for which "P" = 1, and "Q" = −2—and are defined by a similar recurrence relation: in simple terms, the sequence starts with 0 and 1, then each following number is found by adding the number before it to twice the number before that. The first Jacobsthal numbers are: Jacobsthal numbers are defined by the recurrence relation: The next Jacobsthal number is also given by the recursion formula:

neg: 21 (number) goes to infinity, thus formula_4 fails to hold for sufficiently large "n". In fact, For every "n" > 2, we have and so formula_4 fails to hold when "n" > 273 (actually, when "n" > 33). Just check a few numbers to see that "n" = 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 21. 21 appears in the Padovan sequence, preceded by the terms 9, 12, 16 (it is the sum of the first two of these). 21 is: 21 (number) 21 (twenty-one) is the natural number following 20 and preceding 22. 21 is: Note that

neg: Gijswijt's sequence the formula_1rd term. The process to generate terms in the sequence can be defined by looking at the sequence as a series of letters in the alphabet of natural numbers: The sequence is base-agnostic. That is, if a run of 10 repeated blocks is found, the next term in the sequence would be a single number 10, not a 1 followed by a 0. The sequence begins with 1 by definition. The 1 in the second term then represents the length 1 of the block of 1s that is found immediately before it in the first term. The 2 in

neg: Knot theory of a given crossing number increases rapidly, making tabulation computationally difficult . Tabulation efforts have succeeded in enumerating over 6 billion knots and links . The sequence of the number of prime knots of a given crossing number, up to crossing number 16, is 0, 0, 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, 46972, 253293, 1388705... . While exponential upper and lower bounds for this sequence are known, it has not been proven that this sequence is strictly increasing . The first knot tables by Tait, Little, and Kirkman used knot diagrams, although Tait also used

neg: Collatz conjecture the cycle is not unique, each permutation's fraction being the next number in the loop cycle: Also, for uniqueness, the parity sequence should be "prime", i.e., not partitionable into identical sub-sequences. For example, parity sequence (1 1 0 0 1 1 0 0) can be partitioned into two identical sub-sequences (1 1 0 0)(1 1 0 0). Calculating the 8-element sequence fraction gives But when reduced to lowest terms {5/7}, it is the same as that of the 4-element sub-sequence And this is because the 8-element parity sequence actually represents two circuits of the loop cycle defined by the 4-element

neg: Wieferich prime is a trivial solution) It is a conjecture that every natural number "k" = a(1) > 1 makes this sequence become periodic, for example, let a(1) = 2: Let a(1) = 83: Let a(1) = 59 (a longer sequence): However, there are many values of a(1) with unknown status, for example, let a(1) = 3: Let a(1) = 14: Let a(1) = 39 (a longer sequence): It is unknown that values for a(1) > 1 exist such that the resulting sequence does not eventually become periodic. When a("n" − 1)="k", a("n") will be (start with "k" = 2): 1093, 11,

neg: Sequential time of the world) was the first fully palindromic time sequence of the twenty-first century. The next palindromic time sequence will be at 02:02:10 at 11/01/2020 (two minutes and twenty-one seconds past 2 AM on 11 January 2020 in most of the world). A sequential time occurred during Pi Day on 3/14/15 at 9:26:53.58979... following the sequence of pi to all digits. Sequential time A sequential time is one in which the numbers form a normal sequence, such as 1:02:03 4/5/06 (two minutes and three seconds past 1 AM on 4 May 2006 [or April 5, 2006 in the United States]

neg: Prüfer sequence we append 5 to the sequence. We are left with only two vertices, so we stop. The tree's sequence is {4,4,4,5}. Let codice_1 be a Prüfer sequence: The tree will have codice_2 nodes, numbered from codice_3 to codice_2. For each node set its degree to the number of times it appears in the sequence plus 1. For instance, in pseudo-code: Next, for each number in the sequence codice_5, find the first (lowest-numbered) node, codice_6, with degree equal to 1, add the edge codice_7 to the tree, and decrement the degrees of codice_6 and codice_5. In pseudo-code: At the end of

neg: Classful network addresses had the two most-significant bits set to 1 and 0 respectively. For these networks, the network address was given by the next 14 bits of the address, thus leaving 16 bits for numbering host on the network for a total of addresses per network. "Class C" was defined with the 3 high-order bits set to 1, 1, and 0, and designating the next 21 bits to number the networks, leaving each network with 256 local addresses. The leading bit sequence "111" designated an at-the-time unspecified addressing mode (""escape to extended addressing mode""), which was later subdivided as Class D

neg: Jacobsthal number the closed-form equation: The first Jacobsthal-Lucas numbers are: Jacobsthal number In mathematics, the Jacobsthal numbers are an integer sequence named after the German mathematician Ernst Jacobsthal. Like the related Fibonacci numbers, they are a specific type of Lucas sequence formula_1 for which "P" = 1, and "Q" = −2—and are defined by a similar recurrence relation: in simple terms, the sequence starts with 0 and 1, then each following number is found by adding the number before it to twice the number before that. The first Jacobsthal numbers are: Jacobsthal numbers are defined by the recurrence relation: The next Jacobsthal

neg: TCP congestion control a packet (e.g. with sequence number 1), the receiver sends an acknowledgement by adding 1 to the sequence number (i.e. acknowledgement number 2). This indicates to the sender that the receiver received the packet number 1 and it expects packet number 2. Suppose that three subsequent packets are lost. The next packets the receiver sees are packet numbers 5 and 6. After receiving packet number 5, the receiver sends an acknowledgement, but still only for sequence number 2. When the receiver receives packet number 6, it sends yet another acknowledgement value of 2. "Duplicate acknowledgement" occurs when the sender receives

neg: Nim A sample game of 21 in which the second player follows the winning strategy: A similar version is the "100 game": two players start from 0 and alternately add a number from 1 to 10 to the sum. The player who reaches 100 wins. The winning strategy is to reach a number in which the digits are subsequent (e.g. 01, 12, 23, 34...) and control the game by jumping through all the numbers of this sequence. Once reached 89, the opponent has lost; they can only choose numbers from 90 to 99, and the next answer can in any case

neg: Miwin's dice against IX, and IX against XI. Third set: fourth set: The probability that a given die in the first sequence (5, 3, 1, 5) or the second sequence (6, 4, 2, 6) will roll a higher number than the next in the sequence is 5/9; a lower number, 4/9. The dice in the first and second Miwin sets have similar attributes: each die bears each of its numbers exactly once, the sum of the numbers is 30, and each number from 1 to 9 is spread twice over the three dice. This attribute characterizes the implementation of intransitive dice, enabling

neg: Maya calendar sequence continues onwards, so the next days in the sequence are 1 Ix, 2 Men, 3 K'ib', 4 Kab'an, 5 Etz'nab', 6 Kawak and 7 Ajaw. With all twenty named days used, these now began to repeat the cycle while the number sequence continues, so the next day after 7 Ajaw is 8 Imix'. The repetition of these interlocking 13- and 20-day cycles therefore takes 260 days to complete (that is, for every possible combination of number/named day to occur once). The earliest known inscription with a Tzolk'in is an Olmec earspool with 2 Ahau 3 Ceh - 6.3.10.9.0, September

neg: Inger Christensen game we play with a world that plays its own game with us.” In the 1981 poetry collection "Alfabet", Christensen used the alphabet (from a ["apricots"] to n ["nights"]) along with the Fibonacci mathematical sequence in which the next number is the sum of the two previous ones (0, 1, 1, 2, 3, 5, 8, 13, 21, 34…). As she explained: "The numerical ratios exist in nature: the way a leek wraps around itself from the inside, and the head of a snowflower, are both based on this series." Her system ends on the n, suggesting many possible meanings including

neg: Decimal floating point are "11", then the 8-bit exponent field is shifted 2 bits to the right (after both the sign bit and the "11" bits thereafter), and the represented significand is in the remaining 21 bits. In this case there is an implicit (that is, not stored) leading 3-bit sequence "100" in the true significand: The "11" 2-bit sequence after the sign bit indicates that there is an "implicit" "100" 3-bit prefix to the significand. Note that the leading bits of the significand field do "not" encode the most significant decimal digit; they are simply part of a larger pure-binary number. For

neg: Complete sequence of 2. Below is a list of the better-known complete sequences. Just as the powers of two form a complete sequence due to the binary numeral system, in fact any complete sequence can be used to encode integers as bit strings. The rightmost bit position is assigned to the first, smallest member of the sequence; the next rightmost to the next member; and so on. Bits set to 1 are included in the sum. These representations may not be unique. For example, in the Fibonacci arithmetic system, based on the Fibonacci sequence, the number 17 can be encoded in six

neg: Collatz conjecture 6480. Collatz conjecture The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer "n". Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of "n", the sequence will always reach 1. The conjecture is named after Lothar Collatz, who introduced the idea in 1937, two years after receiving

neg: Collatz conjecture Collatz conjecture The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer "n". Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of "n", the sequence will always reach 1. The conjecture is named after Lothar Collatz, who introduced the idea in 1937, two years after receiving his

neg: Paradoxes of set theory finished after one hour. Obviously the set of balls in the reservoir increases without bound. Nevertheless, after one hour the reservoir is empty because for every ball the time of removal is known. The paradox is further increased by the significance of the removal sequence. If the balls are not removed in the sequence 1, 2, 3, ... but in the sequence 1, 11, 21, ... after one hour infinitely many balls populate the reservoir, although the same amount of material as before has been moved. For all its usefulness in resolving questions regarding infinite sets, naive set theory has

neg: Normal number strings of equal length occur with equal asymptotic frequency. For example, in a normal binary sequence (a sequence over the alphabet {0,1}), 0 and 1 each occur with frequency ⁄; 00, 01, 10, and 11 each occur with frequency ⁄; 000, 001, 010, 011, 100, 101, 110, and 111 each occur with frequency ⁄, etc. Roughly speaking, the probability of finding the string "w" in any given position in "S" is precisely that expected if the sequence had been produced at random. Suppose now that "b" is an integer greater than 1 and "x" is a real number. Consider the

neg: Bistritz stability criterion polynomial can be declared not stable as soon as a formula_31, or a formula_32, or a change of sign in the sequence of formula_33's is observed. Consider the polynomial formula_34, where formula_35 is a real parameter. Q1:For what values of formula_35 the polynomial is stable? Construct the sequence: Use their values at z=1 to form All the entries in the sequence are positive for -4 < K < 22 (and for no "K" are they all negative). Therefore D(z) is stable for −4 < "K" < 22. Q2: Find ZL for K = 33 Var { 71, 11, -48, 11

neg: Stop-and-wait ARQ to 1) in subsequent frames. When the receiver sends an ACK, it includes the sequence number of the next packet it expects. This way, the receiver can detect duplicated frames by checking if the frame sequence numbers alternate. If two subsequent frames have the same sequence number, they are duplicates, and the second frame is discarded. Similarly, if two subsequent ACKs reference the same sequence number, they are acknowledging the same frame. Stop-and-wait ARQ is inefficient compared to other ARQs, because the time between packets, if the ACK and the data are received successfully, is twice the transit time (assuming

neg: Turing's proof unsuccessful computating machine. It fails to print, ad infinitum, the figures 0 or 1 that represent in binary the number it computes 8 circle-free — a successful computating machine. It prints, ad infinitum, the figures 0 or 1 that represent in binary the number it computes 9 sequence — as in “sequence computed by the machine”: symbols of the first kind a.k.a. figures a.k.a. symbols 0 and 1. 10 computable sequence — can be computed by a circle-free machine 11 S.D – Standard Description: a sequence of symbols A, C, D, L, R, N, “;” on a Turing machine tape

neg: Kolakoski sequence it outputs "x" copies of the number 1, while if "i" is even, it outputs "x" copies of the number 2. Thus, the first few steps of the algorithm are: This algorithm takes linear time, but because it needs to refer back to earlier positions in the sequence it needs to store the whole sequence, taking linear space. An alternative algorithm that generates multiple copies of the sequence at different speeds, with each copy of the sequence using the output of the previous copy to determine what to do at each step, can be used to generate the sequence in

neg: Calkin–Wilf tree next fraction in the sequence. The Calkin–Wilf sequence can also be generated directly by the formula where formula_2 denotes the "i"th number in the sequence, starting from formula_3, and formula_4 represents the integral part. It's also possible to calculate formula_2 directly from the run-length encoding of the binary representation of : the number of consecutive 1-digits starting from the least significant bit, then the number of consecutive 0-digits starting from the first block of 1-digits, etc. The sequence of numbers generated in this way gives the continued fraction representation of formula_2. Example:<br> i = 1081 = formula_7: The continued fraction

neg: Hyperperfect number numbers that are not perfect are 21, 301, 325, 697, 1333, ... . The following table lists the first few "k"-hyperperfect numbers for some values of "k", together with the sequence number in the On-Line Encyclopedia of Integer Sequences (OEIS) of the sequence of "k"-hyperperfect numbers: It can be shown that if "k" > 1 is an odd integer and "p" = (3"k" + 1) / 2 and "q" = 3"k" + 4 are prime numbers, then "p"²"q" is "k"-hyperperfect; Judson S. McCranie has conjectured in 2000 that all "k"-hyperperfect numbers for odd "k" > 1 are of this form,

neg: Long division division of 500 by 4 (with a result of 125). In the above example, the first step is to find the shortest sequence of digits starting from the left end of the dividend, 500, that the divisor 4 goes into at least once; this shortest sequence in this example is simply the first digit, 5. The largest number that the divisor 4 can be multiplied by without exceeding 5 is 1, so the digit 1 is put above the 5 to start constructing the quotient. Next, the 1 is multiplied by the divisor 4, to obtain the largest whole number

neg: Einsatzgruppen reports Soviet Jews took place on September 29, 1941, in the ravine of Babi Yar near Kiev, where 33,771 Jews of all ages were machine-gunned (Situation Report No. 101). After World War II, the reports were grouped and numbered by the Allies in order to summarize their content. The actual German cables were sent in their own differing sequence including by the "Einsatzgruppe" A (EG–A) attached to Army Group North, "Einsatzgruppe" B (EG–B) attached to Army Group Center, "Einsatzgruppe" C (EG-C) attached to the Army Group South, and "Einsatzgruppe" D (EG–D) attached to the 11th Army. In the OSRs, individual "Ereignismeldungen

neg: Hyperperfect number Hyperperfect number In mathematics, a "k"-hyperperfect number is a natural number "n" for which the equality "n" = 1 + "k"("σ"("n") − "n" − 1) holds, where "σ"("n") is the divisor function (i.e., the sum of all positive divisors of "n"). A hyperperfect number is a "k"-hyperperfect number for some integer "k". Hyperperfect numbers generalize perfect numbers, which are 1-hyperperfect. The first few numbers in the sequence of "k"-hyperperfect numbers are 6, 21, 28, 301, 325, 496, 697, ... , with the corresponding values of "k" being 1, 2, 1, 6, 3, 1, 12, ... . The first few "k"-hyperperfect

neg: 21 (drinking game) the proposal of the game depending on personal rules; this is due to some variants calling for "any" person who says the number "21" to drink. For example: As the game progresses, each player in turn must recite one to four numbers, counting in sequence from where the previous player left off: If a player makes a mistake, then they suffer a small to moderate drinking penalty (e.g. 2 fingers of drink) and then restart the game from 1. Mistakes include: Assuming there are no mistakes, the game will continue in sequence up to 21. The player who calls 21

neg: Hyperperfect number -δ("n") for at least one "j" > 0. Hyperperfect number In mathematics, a "k"-hyperperfect number is a natural number "n" for which the equality "n" = 1 + "k"("σ"("n") − "n" − 1) holds, where "σ"("n") is the divisor function (i.e., the sum of all positive divisors of "n"). A hyperperfect number is a "k"-hyperperfect number for some integer "k". Hyperperfect numbers generalize perfect numbers, which are 1-hyperperfect. The first few numbers in the sequence of "k"-hyperperfect numbers are 6, 21, 28, 301, 325, 496, 697, ... , with the corresponding values of "k" being 1, 2, 1, 6, 3,

neg: Flow control (data) having to wait for an acknowledgement. A sequence number is assigned to frames in order to help keep track of those frames which did receive an acknowledgement. The receiver acknowledges a frame by sending an acknowledgement that includes the sequence number of the next frame expected. This acknowledgement announces that the receiver is ready to receive n frames, beginning with the number specified. Both the sender and receiver maintain what is called a window. The size of the window is less than or equal to the buffer size. Sliding window flow control has a far better performance than stop-and-wait flow

neg: Old School RuneScape The player controls a single character and can interact with NPCs, objects, and entities in the game world by left-clicking, or selecting an option from the object's right-click menu, since many objects can offer more than one interaction option. Due to the game's simple interface and gameplay mechanics, "OSRS" has a relatively low bar of entry as opposed to "RuneScape" or other more complex MMOs. Coupled with the fact that there is a large free-to-play section of the game, it is a popular first game for players that are new to online games. "OSRS" offers an "Ironman" gamemode wherein players

neg: Golden ratio base Golden ratio base Golden ratio base is a non-integer positional numeral system that uses the golden ratio (the irrational number ≈ 1.61803399 symbolized by the Greek letter φ) as its base. It is sometimes referred to as base-φ, golden mean base, phi-base, or, colloquially, phinary. Any non-negative real number can be represented as a base-φ numeral using only the digits 0 and 1, and avoiding the digit sequence "11" – this is called a "standard form". A base-φ numeral that includes the digit sequence "11" can always be rewritten in standard form, using the algebraic properties of the base φ

neg: Hull number example, there have been at least eight vessels named , but CV-6 uniquely identifies the World War II aircraft carrier from all others. For convenience, the combined designation, which is painted on the sides of the hulls, is frequently called the "hull number". The official Navy Style Guide says that hull numbers do not include hyphens. The U.S. Navy sometimes ignores the sequence of hull numbering. For example, the Navy built the last nuclear submarine as . Next the Navy built the three "Seawolf"-class submarines SSN-21 through SSN-23. Then the Navy later resumed the original sequence of hull numbers with

neg: Persistence of a number persistence 0, 1, ... are: The next number in the sequence (the smallest number of additive persistence 5) is 2 × 10 − 1 (that is, 1 followed by 2222222222222222222222 9's). For any fixed base, the sum of the digits of a number is proportional to its logarithm; therefore, the additive persistence is proportional to the iterated logarithm. More about the additive persistence of a number can be found here. Persistence of a number In mathematics, the persistence of a number is the number of times one must apply a given operation to an integer before reaching a fixed point

neg: Divisibility rule ... (mod 7). Take each digit of the number (371) in reverse order (173), multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repeating with this sequence of multipliers as long as necessary (1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, ...), and adding the products (1×1 + 7×3 + 3×2 = 1 + 21 + 6 = 28). The original number is divisible by 7 if and only if the number obtained using this procedure is divisible by 7 (hence 371 is divisible by 7 since 28 is). This method can be

neg: Seamus Heaney Collected Poems Oratory 10. Girls Bathing, Galway, 1965 11. Requiem for the Croppies 12. Rite of Spring 13. Undine 14. The Wife's Tale 15. Mother 16. Cana Revisited 17. Elegy for a Stillborn Child 18. Victorian Guitar 19. Night Drive 20. At Ardboe Point 21. Relic of Memory 22. A Lough Neagh Sequence 1. Up the Shore 23. A Lough Neagh Sequence 2. Beyond Sargasso 24. A Lough Neagh Sequence 3. Bait 25. A Lough Neagh Sequence 4. Setting 26. A Lough Neagh Sequence 5. Lifting 27. A Lough Neagh Sequence 6. The Return 28. A Lough Neagh Sequence 7. Vision 29.

neg: Deficient number Deficient number In number theory, a deficient or deficient number is a number "n" for which the sum of divisors "σ"("n")<2"n", or, equivalently, the sum of proper divisors (or aliquot sum) "s"("n")<"n". The value 2"n" − "σ"("n") (or "n" − "s"("n")) is called the number's deficiency. The first few deficient numbers are: As an example, consider the number 21. Its proper divisors are 1, 3 and 7, and their sum is 11. Because 11 is less than 21, the number 21 is deficient. Its deficiency is 2 × 21 − 32 = 10. Closely related to deficient numbers are perfect

neg: HIKESHI organism that is further removed evolutionarily from another organism is likely to display a greater divergence in the sequence of the orthologs being studied. Table of Chromosome 11 open reading frame 73 Orthologs The table shows the 13 sequences (12 orthologs, 1 original sequence) along with protein name, accession numbers, nucleotide identity, protein identity, and E-values. The accession numbers are the identification numbers from the NCBI Protein database. The nucleotide sequence can be accessed from the protein’s sequence page from DBSOURCE, which gives the accession number and is a link to the nucleotide’s sequence page. The length of both the

neg: Lehmer code 1, …, "n", then it is encoded by a sequence of "n" numbers, but not all such sequences are valid since every number must be used only once. By contrast the encodings considered here choose the first number from a set of "n" values, the next number from a fixed set of values, and so forth decreasing the number of possibilities until the last number for which only a single fixed value is allowed; "every" sequence of numbers chosen from these sets encodes a single permutation. While several encodings can be defined, the Lehmer code has several additional useful properties;

neg: In-place matrix transposition data motion). Next, the value in position 1 (in the original storage: 11, 12, 13, 14, 21, 22, 23, 24) goes to position 2 (in the transposed storage 11, 21, 12, 22, 13, 23, 14, 24), while the value in position 2 (11, 12, 13, 14, 21, 22, 23, 24) goes to position 4 (11, 21, 12, 22, 13, 23, 14, 24), and position 4 (11, 12, 13, 14, 21, 22, 23, 24) goes back to position 1 (11, 21, 12, 22, 13, 23, 14, 24). Similarly for the values in position 7 and positions (3 6 5). In the

neg: 0.999... number. In particular "0.333...;...000..." and "0.999...;...000..." do not correspond to any number. The standard definition of the number 0.999... is the limit of the sequence 0.9, 0.99, 0.999, ... A different definition involves what Terry Tao refers to as "ultralimit", i.e., the equivalence class [(0.9, 0.99, 0.999, ...)] of this sequence in the ultrapower construction, which is a number that falls short of 1 by an infinitesimal amount. More generally, the hyperreal number with last digit 9 at infinite hypernatural rank "H", satisfies a strict inequality Accordingly, an alternative interpretation for "zero followed by infinitely many 9s" could be All

neg: What Makes a Good Man? twenty-one seconds, was uploaded on 21 August 2012 to the band's Vevo channel on YouTube. What Makes a Good Man? "What Makes a Good Man?" is a song by English rock band The Heavy. It was released as the lead single from their third studio album, "The Glorious Dead", on 23 May 2012. A music video for the song was also released on Vevo and YouTube on 21 August 2012. The song peaked at number 127 on the French Singles Chart. The song was also used during the credits sequence in the video game "". and a Russian television commercial

neg: Star number 1 or 4, and progresses in the sequence 1, 4, 1. The last two digits of a star number in base 10 are always 01, 13, 21, 33, 37, 41, 53, 61, 73, 81, or 93. Unique among the star numbers is 35113, since its prime factors (i.e. 13, 37 and 73) are also consecutive star numbers. Geometrically, the "n"th star number is made up of a central point and 12 copies of the ("n"−1)th triangular number — making it numerically equal to the "n"th centered dodecagonal number, but differently arranged. Infinitely many star numbers are also triangular numbers, the

neg: Stop-and-wait ARQ has such a long latency that the sender's timeout runs out before the frame reaches the receiver. In this case the sender resends the same packet. Eventually the receiver gets two copies of the same frame, and sends an ACK for each one. The sender, waiting for a single ACK, receives two ACKs, which may cause problems if it assumes that the second ACK is for the next frame in the sequence. To avoid these problems, the most common solution is to define a 1 bit "sequence number" in the header of the frame. This sequence number alternates (from 0

neg: Robust Header Compression essentially static and pseudo-dynamic compression. In Second-Order (SO) state, the compressor is suppressing all dynamic fields such as RTP sequence numbers, and sending only a logical sequence number and partial checksum to cause the other side to predictively generate and verify the headers of the next expected packet. In general, FO state compresses all static fields and most dynamic fields. SO state is compressing all dynamic fields predictively using a sequence number and checksum. Transitions between the above states occur when the compressor: A typical ROHC implementation will aim to get the terminal into Second-Order state, where a 1-byte ROHC

neg: Odd greedy expansion have posed the question of whether the odd greedy algorithm terminates with a finite expansion for every "x"/"y" with "y" odd. , this question remains open. Applying the odd greedy algorithm to a fraction with an even denominator produces an infinite series expansion. For instance Sylvester's sequence can be viewed as generated by the odd greedy expansion of 1/2. Let "x"/"y" = 4/23. 23/4 = 5 3/4; the next larger odd number is 7. So in the first step, we expand 161/5 = 32 1/5; the next larger odd number is 33. So in the next step, we expand 5313/4

neg: Lucas pseudoprime to use trial and error to find the first "D" in the sequence 5, −7, 9, −11, ... such that formula_3 is −1. (If "D" and "n" have a prime factor in common, then formula_23). With this sequence of "D" values, the average number of "D" values that must be tried before we encounter one whose Jacobi symbol is −1 is about 1.79; see, p. 1416. Once we have "D", we set "P" = 1 and formula_24. It is a good idea to check that "n" has no prime factors in common with "P" or "Q". This method of choosing

neg: Generalizations of Fibonacci numbers Generalizations of Fibonacci numbers In mathematics, the Fibonacci numbers form a sequence defined recursively by: That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci sequence has been studied extensively and generalized in many ways, for example, by starting with other numbers than 0 and 1, by adding more than two numbers to generate the next number, or by adding objects other than numbers. Using , one can extend the Fibonacci numbers to negative integers. So we get: and . See also Negafibonacci. There are a number of possible generalizations of the

neg: Generalizations of Fibonacci numbers numbers" which occur as formula_36. Generalizations of Fibonacci numbers In mathematics, the Fibonacci numbers form a sequence defined recursively by: That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci sequence has been studied extensively and generalized in many ways, for example, by starting with other numbers than 0 and 1, by adding more than two numbers to generate the next number, or by adding objects other than numbers. Using , one can extend the Fibonacci numbers to negative integers. So we get: and . See also Negafibonacci. There are a number

neg: CRISPR spacers in different CRISPR arrays is typically 32 to 38 bp (range 21 to 72 bp). New spacers can appear rapidly as part of the immune response to phage infection. There are usually fewer than 50 units of the repeat-spacer sequence in a CRISPR array. Small clusters of "cas" genes are often located next to CRISPR repeat-spacer arrays. Collectively the 93 "cas" genes are grouped into 35 families based on sequence similarity of the encoded proteins. 11 of the 35 families form the "cas" core, which includes the protein families Cas1 through Cas9. A complete CRISPR-Cas locus has at least

neg: Gauss's lemma (number theory) number of these residues that are greater than . Then where formula_3 is the Legendre symbol. Taking = 11 and = 7, the relevant sequence of integers is After reduction modulo 11, this sequence becomes Three of these integers are larger than 11/2 (namely 6, 7 and 10), so = 3. Correspondingly Gauss's lemma predicts that This is indeed correct, because 7 is not a quadratic residue modulo 11. The above sequence of residues may also be written In this form, the integers larger than 11/2 appear as negative numbers. It is also apparent that the absolute values of the

neg: Vehicle registration plates of Malaysia allow further W plates, the algorithm was altered to feature an alphabetical suffix behind the number sequence, resetting at "W 1 A". When "W 9999 Y" was achieved, the second alphabetical sequence emerged between the state prefix and number sequence, leading to "WA 1 A". When "WA 9999 Y" is met, the first alphabetical sequence will reset and the second alphabetical sequence will advance, giving "WB 1 A". When "WY 9999 Y" is reached, a third new alphabetical sequence will be spliced into the algorithm, between the second alphabetical sequence and number sequence, resulting in "WAA 1 A". The series

neg: Sign sequence made by German mathematician Uwe Stroinski on Tao's blog. His proof was published in 2016, as the first paper in the new journal "Discrete Analysis". A Barker code is a sequence of "N" values of +1 and −1, such that for all formula_5. Barker codes of lengths 11 and 13 are used in direct-sequence spread spectrum and pulse compression radar systems because of their low autocorrelation properties. Sign sequence In mathematics, a sign sequence, or ±1–sequence or bipolar sequence, is a sequence of numbers, each of which is either 1 or −1. One example is the sequence (1, −1, 1,

neg: Service number (United States Army) 7, 8, 9, and 0) were unassigned and used by various recruiting stations outside the United States. The 11 000 000 through 19 999 999 series were issued to enlisted personnel who had enlisted within the boundaries of the 48 contiguous states and the territory of Alaska after 1 July 1940. The second number was determined by what group of states a person was recruited from, the next six were an identifying number for the service member; thus, for each geographical area there was an available range of 999,999 service numbers. The various geographical number codes were as follows: 11:

neg: Telephone numbers in Brazil customer service numbers have been normatized as "103", followed by a two-digit code. For example, Embratel customers contact the company's customer service dialing "103-21". For most mobile carriers, the number is "105", followed by a one-digit code (e.g., "105-2" for Claro). For cable and satellite television operators, the number is "106", followed by a two-digit code (e.g., "106-21" for Net and "106-11" for SKY Brasil). The Brazilian system for long-distance dialing is relatively unusual and somewhat confusing, insofar as the choice of long-distance carrier determines the actual digit sequence to be dialed. The standard format for writing down — but

neg: Quaternary numeral system alphabetical order, abbreviated A, C, G and T, can be taken to represent the quaternary digits in numerical order 0, 1, 2, and 3. With this encoding, the complementary digit pairs 0↔3, and 1↔2 (binary 00↔11 and 01↔10) match the complementation of the base pairs: A↔T and C↔G and can be stored as data in DNA sequence. For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010 (= decimal 9156 or binary 10 00 11 11 00 01 00). Quaternary line codes have been used for transmission, from the invention of the telegraph to the 2B1Q

neg: Rank-size distribution a much larger number of cities orders of magnitude smaller. For example, a rank 3 city would have one-third the population of a country's largest city, a rank 4 city would have one-fourth the population of the largest city, and so on. When any log-linear factor is ranked, the ranks follow the Lucas numbers, which consist of the sequentially additive numbers 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, etc. Like the more famous Fibonacci sequence, each number is approximately 1.618 (the Golden ratio) times the preceding number. For example, the third term in the sequence above,

neg: What a Girl Wants (Christina Aguilera song) at number 18 on the US Hot Dance Club Songs chart where it spent 11 weeks. The single was certified Gold by the Recording Industry Association of America (RIAA) and has sold over 600,000 copies in the US to date. In Oceania, the song performed well. In Australia, the track debuted at number 21 on the issue date of January 9, 2000, where it stayed for a further week. For the next two weeks the single rose up the charts before making its peak at number five on the charts. The track spent a total of 18 weeks on the

neg: Fib (poetry) 21-line poems, that follow a 1/1/2/3/5/8/13 structure and total 99 syllables. Marcia Birken and Anne C. Coon also discussed the fibonacci number sequence in their groundbreaking book, Discovering Patterns in Mathematics and Poetry. As Deborah Haar Clark has noted, "Fibonacci poetry is not new. It’s been around in one form or another for centuries, with works applying the numerical sequence to syllables, words, or letters." However, the six-line, 20-syllable fib itself was brought to wider public attention by Gregory K. Pincus on 1 April 2006. His blog has been the center of this new form of poetry. After Pincus published

neg: Sequence 1, 8, 27, …) and formula_48 (which begins -1, 1, -1, 1, …) are both divergent. If a sequence converges, then the value it converges to is unique. This value is called the limit of the sequence. The limit of a convergent sequence formula_34 is normally denoted formula_50. If formula_34 is a divergent sequence, then the expression formula_50 is meaningless. A sequence of real numbers formula_34 converges to a real number formula_41 if, for all formula_55, there exists a natural number formula_56 such that for all formula_57 we have formula_58 If formula_34 is a sequence of complex numbers rather than

neg: Binary number into the first three digits 110 of the dividend one time, so a "1" is written on the top line. This result is multiplied by the divisor, and subtracted from the first three digits of the dividend; the next digit (a "1") is included to obtain a new three-digit sequence: The procedure is then repeated with the new sequence, continuing until the digits in the dividend have been exhausted: Thus, the quotient of 11011 divided by 101 is 101, as shown on the top line, while the remainder, shown on the bottom line, is 10. In decimal, 27 divided by

neg: Fourier analysis that it often provides insight into the amount of aliasing caused by the sampling process. Applications of the DTFT are not limited to sampled functions. See Discrete-time Fourier transform for more information on this and other topics, including: Similar to a Fourier series, the DTFT of a periodic sequence, , with period , becomes a Dirac comb function, modulated by a sequence of complex coefficients (see DTFT/Periodic data): The sequence is what is customarily known as the DFT of _{\triangleq\, \frac{1}{T} S_\frac{1}{T}\left(\frac{k}{NT}\right)}</math> </ref> Conversely, when one wants to compute an arbitrary number () of discrete samples of one cycle of

neg: Steinhaus–Johnson–Trotter algorithm the numbers 1 and 2), as may be shown by induction. Although this sequence may be generated by a recursive algorithm that constructs the sequence of smaller permutations and then performs all possible insertions of the largest number into the recursively-generated sequence, the actual Steinhaus–Johnson–Trotter algorithm avoids recursion, instead computing the same sequence of permutations by an iterative method. As described by , the algorithm for generating the next permutation from a given permutation π performs the following steps When no number "i" can be found meeting the conditions of the second step of the algorithm, the algorithm has reached

neg: Palindromic number types of palindromic numbers these values are listed below in a table. Here 0 is included. There are many palindromic perfect powers "n", where "n" is a natural number and "k" is 2, 3 or 4. The first nine terms of the sequence 1, 11, 111, 1111, ... form the palindromes 1, 121, 12321, 1234321, ... The only known non-palindromic number whose cube is a palindrome is 2201, and it is a conjecture the fourth root of all the palindrome fourth powers are a palindrome with 100000...000001 (10 + 1). G. J. Simmons conjectured there are no palindromes of form

neg: Rudin–Shapiro sequence For example, "a" = 1 and "b" = −1 because the binary representation of 6 is 110, which contains one occurrence of 11; whereas "a" = 2 and "b" = +1 because the binary representation of 7 is 111, which contains two (overlapping) occurrences of 11. Starting at "n" = 0, the first few terms of the "a" sequence are: and the corresponding terms "b" of the Rudin–Shapiro sequence are: The Rudin–Shapiro sequence can be generated by a four state automaton. There is a recursive definition The values of the terms "a" and "b" in the Rudin–Shapiro sequence can be

neg: String (computer science) is called a "formal language" over Σ. For example, if Σ = {0, 1}, the set of strings with an even number of zeros, {ε, 1, 00, 11, 001, 010, 100, 111, 0000, 0011, 0101, 0110, 1001, 1010, 1100, 1111, ...}, is a formal language over Σ. "Concatenation" is an important binary operation on Σ. For any two strings "s" and "t" in Σ, their concatenation is defined as the sequence of symbols in "s" followed by the sequence of characters in "t", and is denoted "st". For example, if Σ = {a, b, ..., z}, "s" = bear, and

neg: Ulam number 4, because the previous terms must be distinct.) The integer 5 is not an Ulam number, because 5 = 1 + 4 = 2 + 3. The first few terms are There are infinitely many Ulam numbers. For, after the first "n" numbers in the sequence have already been determined, it is always possible to extend the sequence by one more element: is uniquely represented as a sum of two of the first "n" numbers, and there may be other smaller numbers that are also uniquely represented in this way, so the next element can be chosen as the smallest

neg: Ulam number initial 2"s" terms of the sequence, has exactly "s" representations as a sum of two previous numbers. Thus, the Ulam numbers and the ("u", "v")-Ulam numbers are 1-additive sequences. If a sequence is formed by appending the largest number with a unique representation as a sum of two earlier numbers, instead of appending the smallest uniquely representable number, then the resulting sequence is the sequence of Fibonacci numbers. Ulam number An Ulam number is a member of an integer sequence devised by and named after Stanislaw Ulam, who introduced it in 1964. The standard Ulam sequence (the (1, 2)-Ulam sequence)

neg: Marathi language 1,234,567 is written as 12,34,567 and read as "12 lakh 34 Hazara 5 she 67". Every two-digit number after 18 (11 to 18 are predefined) is read backward. For example, 21 is read एक-वीस (1-twenty). Also, a two digit number that ends with a 9 is considered to be the next tens place minus one. For example, 29 is एकुणतीस/एकोणतीस (एक-उणे-तीस)(Thirty minus one). Two digit numbers used before "Hazara", etc. are written in the same way. Shrilipee, Shivaji, kothare 2,4,6, Kiran fonts KF-Kiran and many more (about 48) are clip fonts that were used prior to the introduction of Unicode

neg: What Separates Me from You "wanting to listen to it again and again", saying that the album featured "a lot of creativity and maturation". The album peaked at number 11 on the U.S. "Billboard" 200, becoming A Day to Remember's personal best, as "Homesick" peaked at number 21. The album also charted at number 1 on the UK Rock Album Chart, number 66 on the UK Albums Chart, number 24 on the ARIA Chart in Australia, and number 4 on the German Newcomer Chart. "All I Want" charted on both Billboard's Hot Modern Rock Tracks and Rock Songs charts, at number 12 and number 25,

neg: WHO Drug Dictionary the WHODrug products have been available in a single subscription service called WHODrug Global. WHODrug drug code consist of 11 characters (alphanumeric code). It has 3 parts: Drug Record Number(DrugRecNo), Sequence number 1(Seq1) and Sequence number 2 (Seq2). DrgRecNo consists of 6 characters. It uniquely identifies active moieties, regardless of salt form or plant part and extract. Seq1 is used to uniquely identify different variations (e.g. salts and esters), plant parts and extraction methods, thereby defining active substances or a combination of active substances. WHODrug records sharing the same DrugRecNo and Seq1 contain the same variation/plant part/extract variation of the

neg: Sequence ones made up of rational numbers, real numbers, and complex numbers. The sequence (.9, .99, .999, .9999, ...) approaches the number 1. In fact, every real number can be written as the limit of a sequence of rational numbers, e.g. via its decimal expansion. For instance, is the limit of the sequence (3, 3.1, 3.14, 3.141, 3.1415, ...). A related sequence is the sequence of decimal digits of , i.e. (3, 1, 4, 1, 5, 9, ...). This sequence does not have any pattern that is easily discernible by eye, unlike the preceding sequence, which is increasing. Other notations can

neg: Codex Corbeiensis II Codex Corbeiensis II The Codex Corbeiensis II, designated by ff or 8 (in the Beuron system), is a 5th-century Latin Gospel Book. The text, written on vellum, is a version of the old Latin. The manuscript contains 190 parchment folio with the text of the four Gospels with lacunae (Matt 1:1-11:16; Luke 9:48; 10:20.21; 11:45-12:6.7; John 17:15-18:9; 20:22-21:8). Written in a beautiful round uncial hand. Gospels follow in the sequence: Matthew, Luke, John, Mark. The Latin text of the codex is a representative Western text-type in "itala" recension. The text is akin to preserved in Codex Vercellensis and Codex Veronensis.