list of integer sequences

It was created and maintained by Neil Sloane while researching at AT&T Labs. Zero is often used to represent non-existent sequence elements. (Answer: click here.). Nederlands people remarked how useful they found the book, and how surprising At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous sequence. The date is January or February, 1964. Saying "punch cards" is like saying "hike boots" or "walk stick" or "chew gum".]. on his dissertation, namely 1, 8, 78, 944, (now entry A000435 in the OEIS), and was looking for a formula for the n-th term, in order to determine the rate of growth of the terms. List of integer sequences On-Line Encyclopedia of Integer Sequences 0-9 3x + 1 semigroup A Abundant number Achilles number Alcuin's sequence Almost perfect number Almost prime Alternating factorial Amicable numbers etina This is the acorn from which the OEIS grew. A. Sloane's Handbook of Integer Sequences (1973) Solved OBJECTIVE You will use your knowledge of functions, - Chegg Index entries for sequences related to Chebyshev polynomials. The introductory chapters from N. J. Types of Number Sequences Importance of Rules in Number Patterns and Sequences Simple Sequences Even and Odd Number Sequences Sequence of Triangular Numbers Arithmetic Number Sequences Number Sequence of Square Numbers Number Sequence of Cube Numbers The length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints. Number Tools Integer Sequence Generator Integer sequence generator World's simplest number tool Quickly calculate a list of integers in your browser. To do this, users must first register. Working on a new problem, he always searches the OEIS. SELECT seq FROM seq_1_to_1000; For 0 to 11, do this. The original collection, A Handbook of Integer Sequences, appeared in 1973 and contained 2,372 entries. A positive integer with more divisors than any smaller positive integer. Italiano This facility is essential in a scientific database, in order that questions involving definitions, possible errors, etc., can be discussed. Again, once the book appeared, many further sequences and updates were (If it isn't, submit it and it will probably be added if it is sufficiently interesting - see. Slovenina Last edited on 20 December 2020, at 22:11, On-Line Encyclopedia of Integer Sequences, https://en.wikipedia.org/w/index.php?title=Category:Integer_sequences&oldid=995412079, This page was last edited on 20 December 2020, at 22:11. A natural number in a set that is filtered by a sieve. 4 of The OEIS Foundation Inc..). This was really worrying, Dr. Sloane said. H. C. Williams and Jeffrey Shallit, Factoring integers before computers. During this period, from 1996 to 2009, the database grew Positive integers which are powerful but imperfect. [8] (The sequences mentioned are A000027, A000217, A000292, A000332, A000389, A000579, A000110, A007318, A000058, A000215, A000289, A000324, A234953 (= A001854(n)/n), A000435, A000169, A000142, A000272, A000312, A000111.) Franais The sequences were transferred to punched cards in 1967, and were Generate an integer sequence in MySQL - Stack Overflow Of course, not all even numbers are eban, but enough are to make a good sequence.. over 750 volumes, each the size of the 1995 book. NJAS waited a year, until the {2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, }, {1, 3, 7, 9, 13, 15, 21, 25, 31, 33, }. A sequence is a stream, which computes the value when it is needed. [citation needed]. We dont know., The number 36 was stubborn it was still absent after the sequence had been computed to a billion terms. This site is supported by donations to The OEIS Foundation. Mentions this sequence - see "List of Sequences" in Vol. On-Line Encyclopedia of Integer Sequences, https://en.wikipedia.org/w/index.php?title=List_of_integer_sequences&oldid=1150013967, {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, }, {1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, }. [citation needed]. \textstyle {1 \over 5},{1 \over 4},{1 \over 3},{2 \over 5},{1 \over 2},{3 \over 5},{2 \over 3},{3 \over 4},{4 \over 5} [14] OEIS normalizes the sequences for lexicographical ordering, (usually) ignoring all initial zeros and ones, and also the sign of each element. This line of thought leads to the question "Does sequence An contain the number n?" {24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, }, {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, }, {0, 1, 4, 9, 16, 25, 36, 49, 64, 81, }, {0, 1, 4, 10, 20, 35, 56, 84, 120, 165, }, {0, 1, 5, 14, 30, 55, 91, 140, 204, 285, }, {0, 1, 8, 27, 64, 125, 216, 343, 512, 729, }, {0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, }, {1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, }, {0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381, }, {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, }, {3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, }, {2, 3, 5, 11, 23, 29, 41, 53, 83, 89, }, {1, 7, 10, 13, 19, 23, 28, 31, 32, 44, }, The numbers whose trajectory under iteration of sum of squares of digits map includes, {2, 3, 5, 7, 23, 719, 5039, 39916801, }, A prime number that is one less or one more than a, {1, 4, 11, 16, 24, 29, 33, 35, 39, 45, }. Searching the database for puzzle produces more than 1,700 results. In 2010, it became a moderated wiki and now is run by about 170 international volunteer editors who wrangle 50 or more new submissions a day. This site is supported by donations to The OEIS Foundation. 5 {1, 1, 5, 19, 101, 619, 4421, 35899, 326981, 3301819, 36614981, 442386619, 5784634181, 81393657019, }, {3, 5, 7, 13, 23, 17, 19, 23, 37, 61, }, {6, 12, 18, 20, 24, 28, 30, 36, 40, 42, }, {15, 34, 65, 111, 175, 260, 369, 505, 671, 870, 1105, 1379, 1695, 2056, }, Sum of numbers in any row, column, or diagonal of a magic square of order, {70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, }. The On-Line Encyclopedia of Integer Sequences (OEIS) It does this by using virtual (fake) one column tables. The randomness comes from atmospheric noise, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs. Sloane has personally managed 'his' sequences for almost 40 years, but starting in 2002, a board of associate editors and volunteers has helped maintain the database. 2) 13112221. This database and its associated files are copyright 2023 by The OEIS Foundation Inc.. The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable. You specify the starting integer and the increment, and the worksheet will prompt for every value in sequence. In OEIS lexicographic order, they are: whereas unnormalized lexicographic ordering would order these sequences thus: #3, #5, #4, #1, #2. Beyond this limit values behave like negative numbers: put the maxInteger+1 -- -2147483648 put the maxInteger+2 -- -2147483647. When you look at 48, you see three holes; 88 has four holes in it; 4 has one hole., And 1 has no holes in it. In the current OEIS Wiki, however, email addresses are not made public and a different mechanism is used for contacting contributors. Sequences usually have patterns that allow us to predict what the next term might be. [16], In 2009, the OEIS database was used by Philippe Guglielmetti to measure the "importance" of each integer number. This would indicate how long the activity in this very simple neural network would persist. Hunting through textbooks, reference books, journals, he came close, but no sequence. to be done single-handedly by NJAS. Lucas numbers beginning at 2: L(n) = L(n-1) + L(n-2), L(0) = 2, L(1) = 1. Tagalog In the end, Russ Cox completely rewrote all the programs needed to maintain the database and answer queries - a huge task! , Detecting consecutive integers in a list - Stack Overflow However, the asymptotic formula shows that the linearity is an illusion and in fact a(n)/n ~ log(n)/log(log(n)) goes to infinity. Please go to Sequences From Classic Books. Anyone who says "punch cards" is showing they know nothing about the subject. (2)) Hrvatski Products of two primes, not necessarily distinct. {0, 1, 3, 5, 8, 11, 14, 17, 21, 25, 29, 33, 37, 41, 45, 49 }, {1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, }, {1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, }, {1, 2, 4, 6, 12, 24, 36, 48, 60, 120, }. The OEIS is owned, maintained and supported by The OEIS Foundation Inc. - please give generously! I found this perplexing, Dr. Pudwell said. Recamn's sequence, A005132 The Busy Beaver problem, A060843 The Catalan numbers, A000108 He asked the assembled experts, Does 36 ever appear in this beautiful sequence? Two hours later, Dr. Cox found it at the far reaches of 77 billion terms the 77,534,485,877th term lands on 36. sequence OEIS n_(max) digits discoverer search limit comments alternating factorial A001272 . See also the graph of A066265 = number of semiprimes < 10^n. Suppose the set M is a transitive model of ZFC set theory. Now we have a degree sequence of a tree with n + 2 nodes. Welcome to The On-Line Encyclopedia of Integer Sequences (OEIS) Wiki, Introductory chapters from the 1973 and 1995 books; Supplement 3 to 1973 book, Description of OEIS entries (or, What is the Next Term? and the sequences A053873, "Numbers n such that OEIS sequence An contains n", and A053169, "n is in this sequence if and only if n is not in sequence An". Its very, very simple, he said. An integer for which the average of its positive divisors is also an integer. The Fibonacci sequence, in which every term (starting with the 3rd term) is the sum of the two preceding numbers, is one of the more familiar sequences in the On-Line Encyclopedia of Integer . A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. {1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40}. The value of a(1) (a 1 1 magic square) is 2; a(3) is 1480028129. List of integer sequences - Wikiwand Lietuvi of The On-Line Encyclopedia of Integer Sequences to the Foundation 2 [10] The 200,000th sequence, A200000, was added to the database in November 2011; it was initially entered as A200715, and moved to A200000 after a week of discussion on the SeqFan mailing list,[11][12] following a proposal by OEIS Editor-in-Chief Charles Greathouse to choose a special sequence for A200000. For more information about the Encyclopedia, see the Welcome page. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context. , As a spin-off from the database work, Sloane founded the Journal of Integer Sequences in 1998. , 4) 59. Although some integer sequences have definitions, there is no systematic way to define what it means for an integer sequence to be definable in the universe or in any absolute (model independent) sense. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, }. This is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121}. A very large number of people have contributed to the database, and it would be impossible to thank them individually. The mathematical equivalent to the FBIs voluminous fingerprint files turns 50 this year, with 362,765 entries (and counting). License Agreements, Terms of Use, Privacy Policy. This category includes not only articles about certain types of integer sequences, but also articles about theorems and conjectures pertaining to, and properties of, integer sequences. Number of consecutive integers starting with, First numerator and then denominator of the central. A001358 - OEIS - The On-Line Encyclopedia of Integer Sequences (OEIS) 5. Data Structures Python 3.11.4 documentation , Find common sequence of elements in list of lists {0, 0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, }, Number of triangles with integer sides and perimeter, {12, 18, 20, 24, 30, 36, 40, 42, 48, 54, }, {2, 5, 52, 88, 96, 120, 124, 146, 162, 188, }. Other important examples of sequences include ones made up of rational numbers, real numbers, and complex numbers. It took us over a year to resolve this problem. own, maintain and raise funds to support What Number Comes Next? The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences.It was created and maintained by Neil Sloane while researching at AT&T Labs.He transferred the intellectual property and hosting of the OEIS to the OEIS Foundation in 2009. Develop number familiarity by writing integers. Beyond that say, for the 4 4 4 Rubiks Revenge Gods Number is uncertain, making for a short sequence thus far: 0, 11, 20. In comments, formulas, etc., a(n) represents the nth term of the sequence. {2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, }, {1, 1, 2, 4, 9, 21, 51, 127, 323, 835, }, The number of ways of drawing any number of nonintersecting chords joining, {1, 2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64. Finally, the function returns the list with all the integer sequences. In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers . Integer Sequences - WorksheetWorks.com Deutsch Magyar 1 The On-Line Encyclopedia of Integer Sequences (OEIS) [Incidentally, today these cards are sometimes referred to as "punch cards" (sic). A. Sloane and Simon Plouffe)", "What Number Comes Next? Number Sequences (video lessons, examples and solutions) [9] Welcome - OeisWiki - The On-Line Encyclopedia of Integer Sequences (OEIS) by Academic Press, San Diego. A natural number that equals the sum of the factorials of its decimal digits. and work was begun on moving the database from NJAS's home page at AT&T by at least 10000 entries per year (18000 new sequences were added in 2009 alone). That means, First term = a 1 Second term = a 2 Third term = a 3 . The OEIS was limited to plain ASCII text until 2011, and it still uses a linear form of conventional mathematical notation (such as f(n) for functions, n for running variables, etc.). A Canadian mathematician, Simon Plouffe, offered to help in He published selections from the database in book form twice: These books were well received and, especially after the second publication, mathematicians supplied Sloane with a steady flow of new sequences. Eesti Each n is a member of exactly one of these two sequences, and in principle it can be determined which sequence each n belongs to, with two exceptions (related to the two sequences themselves): This entry, A046970, was chosen because it contains every field an OEIS entry can have. The different numbers occurring in a sequence are called the terms of the sequence.