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### WELCOME - OEISWIKI

Welcome to The On-Line Encyclopedia of Integer Sequences® (OEIS®) Wiki Some Famous Sequences. Click on any of the following to see examples of famous sequences in the On-Line Encyclopedia of Integer Sequences (the OEIS), then hit "Back" in your browser to return here: . Recamán's sequence, A005132 The Busy Beaver problem, A060843 The Catalan numbers, A000108 LIST OF LATEX MATHEMATICAL SYMBOLS Hyperbolic functions The abbreviations arcsinh, arccosh, etc., are commonly used for inverse hyperbolic trigonometric functions (area hyperbolic functions), even though they are misnomers, since the prefix arc is the abbreviation for arcus, while the prefix ar stands### for area.

### A036968 - OEIS

Genocchi numbers (of first kind): expansion of 2*x/ (exp (x)+1). The sign of a (1) depends on which convention one chooses: B (n) = B_n (1) or B (n) = B_n (0) where B (n) are the Bernoulli numbers and B_n (x) the Bernoulli polynomials (see the Wikipedia article on Bernoulli numbers). The definition given is in line with B (n) = B_n (0).### A000010 - OEIS

A000010 Euler totient function phi(n): count numbers 0. 5### A247698 - OEIS

OFFSET: 1,1; COMMENTS: B(n) / B(n - 1) approaches the golden ratio as n approaches infinity. LINKS: Logan Cooper, Table of n, a(n) for n = 1..1000 (truncated from 9966 to 1000 terms by M. F. Hasler, May 10 2017) Brady Haran and Matt Parker, Brady Numbers, Numberphile video (2014) Index entries for linear recurrences with constant coefficients, signature (1,1). ALL SOLUTIONS TO THE PROBLEM OF EIGHT QUEENS All solutions to the problem of eight queens The eight queens problem was apparently ﬁrst proposed by Max Bezzel in the Berliner Schachzeitung (1848) and ﬁrst fully solved by Franz Nauck in Leipziger Illustrierte Zeitung (1850). THE ON-LINE ENCYCLOPEDIA OF INTEGER SEQUENCES® (OEIS®)A005150STYLE SHEETSUPERSEEKERA000040MUSICA001220 The On-Line Encyclopedia of Integer Sequences® (OEIS®) For more information about the Encyclopedia, see the Welcome page. Languages: English Shqip العربية Bangla Български Català 中文 ( 正體字 , 简化字 L'ENCYCLOPÉDIE EN LIGNE DES SUITES DE NOMBRES …TRANSLATE THIS PAGE The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.### WELCOME - OEISWIKI

Welcome to The On-Line Encyclopedia of Integer Sequences® (OEIS®) Wiki Some Famous Sequences. Click on any of the following to see examples of famous sequences in the On-Line Encyclopedia of Integer Sequences (the OEIS), then hit "Back" in your browser to return here: . Recamán's sequence, A005132 The Busy Beaver problem, A060843 The Catalan numbers, A000108 LIST OF LATEX MATHEMATICAL SYMBOLS Hyperbolic functions The abbreviations arcsinh, arccosh, etc., are commonly used for inverse hyperbolic trigonometric functions (area hyperbolic functions), even though they are misnomers, since the prefix arc is the abbreviation for arcus, while the prefix ar stands### for area.

### A036968 - OEIS

Genocchi numbers (of first kind): expansion of 2*x/ (exp (x)+1). The sign of a (1) depends on which convention one chooses: B (n) = B_n (1) or B (n) = B_n (0) where B (n) are the Bernoulli numbers and B_n (x) the Bernoulli polynomials (see the Wikipedia article on Bernoulli numbers). The definition given is in line with B (n) = B_n (0).### A000010 - OEIS

A000010 Euler totient function phi(n): count numbers 0. 5### A247698 - OEIS

OFFSET: 1,1; COMMENTS: B(n) / B(n - 1) approaches the golden ratio as n approaches infinity. LINKS: Logan Cooper, Table of n, a(n) for n = 1..1000 (truncated from 9966 to 1000 terms by M. F. Hasler, May 10 2017) Brady Haran and Matt Parker, Brady Numbers, Numberphile video (2014) Index entries for linear recurrences with constant coefficients, signature (1,1). ALL SOLUTIONS TO THE PROBLEM OF EIGHT QUEENS All solutions to the problem of eight queens The eight queens problem was apparently ﬁrst proposed by Max Bezzel in the Berliner Schachzeitung (1848) and ﬁrst fully solved by Franz Nauck in Leipziger Illustrierte Zeitung (1850). TOOTHPICK-LIKE SEQUENCE EXPLORATION Instructions See the OEIS entries for A139250, A147562, A151723, A151725, A160120, A161644, and A160720 for a description of the toothpick sequence and some other related sequences, and some background. Select a sequence, enter a value of N and click Update to draw the figure after N iterations.. Type selects the type of figure### drawn.

### A000217 - OEIS

The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.### A160338 - OEIS

OFFSET: 1,105; COMMENTS: Different from A137979: first time these sequence disagree is at n=14235 with a(14235)=2 and A137979(14235)=3.; LINKS: Max Alekseyev, Table of n, a(n) for n = 1..100000 Alexandre Kosyak, Pieter Moree, Efthymios Sofos and Bin Zhang, Cyclotomic polynomials with prescribed height and prime number theory, arXiv:1910.01039 , 2019.### A250001 - OEIS

More precisely, there are A000081 (n+1) ways to arrange n circles if no two of them meet. - N. J. A. Sloane, May 16 2017. From Daniel Forgues, Aug 08-09 2015: (Start) A representation for the diagrams in a250001.jpg (in the same order): a (1) = 1: { {2}}; a (2) = 3: { {2, 3}, {2, 4}, {4, 6}};### A007588 - OEIS

The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.### A001235 - OEIS

The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. NUMBER OF DERANGEMENTS Example. You have 6 balls in 6 different colors, and for every ball you have a box of the same color. How many derangements do you have, if no ball is in a box of the same color?### A018226 - OEIS

OFFSET: 1,1; COMMENTS: In the shell model for the nucleus, magic numbers are the numbers of either protons or neutrons at which a shell is filled. First seven positive terms of A162626.- Omar E. Pol, Jul 07 2009 Steppenbeck: "The results of the experiment indicate that 54Ca's first excited state lies at a relatively high energy, which is characteristic of a large nuclear shell gap, thus### A001203 - OEIS

0,1. COMMENTS. The first 5821569425 terms were computed by Eric W. Weisstein on Sep 18 2011. The first 10672905501 terms were computed by Eric W. Weisstein on Jul 17 2013. The first 15000000000 terms were computed by Eric W. Weisstein on Jul 27 2013. The first 30113021586 terms were computed by Syed Fahad on Apr 27 2021.### A001175 - OEIS

OFFSET: 1,2; COMMENTS: These numbers might also have been called Fibonacci periods. Also, number of perfect multi-Skolem type sequences of order n. Index the Fibonacci numbers so THE ON-LINE ENCYCLOPEDIA OF INTEGER SEQUENCES® (OEIS®)A005150STYLE SHEETSUPERSEEKERA000040MUSICA001220 The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. L'ENCYCLOPÉDIE EN LIGNE DES SUITES DE NOMBRES …TRANSLATE THIS PAGE The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. LIST OF LATEX MATHEMATICAL SYMBOLS Hyperbolic functions The abbreviations arcsinh, arccosh, etc., are commonly used for inverse hyperbolic trigonometric functions (area hyperbolic functions), even though they are misnomers, since the prefix arc is the abbreviation for arcus, while the prefix ar stands### for area.

TOOTHPICK-LIKE SEQUENCE EXPLORATION Instructions See the OEIS entries for A139250, A147562, A151723, A151725, A160120, A161644, and A160720 for a description of the toothpick sequence and some other related sequences, and some background. Select a sequence, enter a value of N and click Update to draw the figure after N iterations.. Type selects the type of figure### drawn.

### A229037 - OEIS

OFFSET: 1,3; COMMENTS: Added name "forest fire" to make it easier to locate this sequence. - N.J. A. Sloane, Sep 03 2019. This sequence and A235383 and A235265 were winners in the best new sequence contest held at the OEIS Foundation booth at the 2014 AMS/MAA Joint Mathematics Meetings. - T.D. Noe, Jan 20 2014. See A236246 for indices n such that a(n)=1. - M.F. Hasler, Jan 20 2### A036968 - OEIS

The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.### A160338 - OEIS

OFFSET: 1,105; COMMENTS: Different from A137979: first time these sequence disagree is at n=14235 with a(14235)=2 and A137979(14235)=3.; LINKS: Max Alekseyev, Table of n, a(n) for n = 1..100000 Alexandre Kosyak, Pieter Moree, Efthymios Sofos and Bin Zhang, Cyclotomic polynomials with prescribed height and prime number theory, arXiv:1910.01039 , 2019.### A005845 - OEIS

OFFSET: 1,1; COMMENTS: This uses the definition of "Lucas pseudoprime" by Bruckman, not the one by Baillie and Wagstaff. - R.J. Mathar, Jul 15 2012. Unlike the earlier Baillie-Wagstaff Lucas pseudoprimes A217120, these have significant overlap with the Fermat primality test.For example, the number 82380774001 is both an A005845 Lucas pseudoprime and a Fermat pseudoprime to the first 407### A247698 - OEIS

OFFSET: 1,1; COMMENTS: B(n) / B(n - 1) approaches the golden ratio as n approaches infinity. LINKS: Logan Cooper, Table of n, a(n) for n = 1..1000 (truncated from 9966 to 1000 terms by M. F. Hasler, May 10 2017) Brady Haran and Matt Parker, Brady Numbers, Numberphile video (2014) Index entries for linear recurrences with constant coefficients, signature (1,1).### A038445 - OEIS

The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. THE ON-LINE ENCYCLOPEDIA OF INTEGER SEQUENCES® (OEIS®)A005150STYLE SHEETSUPERSEEKERA000040MUSICA001220 The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. L'ENCYCLOPÉDIE EN LIGNE DES SUITES DE NOMBRES …TRANSLATE THIS PAGE The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. LIST OF LATEX MATHEMATICAL SYMBOLS Hyperbolic functions The abbreviations arcsinh, arccosh, etc., are commonly used for inverse hyperbolic trigonometric functions (area hyperbolic functions), even though they are misnomers, since the prefix arc is the abbreviation for arcus, while the prefix ar stands### for area.

TOOTHPICK-LIKE SEQUENCE EXPLORATION Instructions See the OEIS entries for A139250, A147562, A151723, A151725, A160120, A161644, and A160720 for a description of the toothpick sequence and some other related sequences, and some background. Select a sequence, enter a value of N and click Update to draw the figure after N iterations.. Type selects the type of figure### drawn.

### A229037 - OEIS

OFFSET: 1,3; COMMENTS: Added name "forest fire" to make it easier to locate this sequence. - N.J. A. Sloane, Sep 03 2019. This sequence and A235383 and A235265 were winners in the best new sequence contest held at the OEIS Foundation booth at the 2014 AMS/MAA Joint Mathematics Meetings. - T.D. Noe, Jan 20 2014. See A236246 for indices n such that a(n)=1. - M.F. Hasler, Jan 20 2### A036968 - OEIS

The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.### A160338 - OEIS

OFFSET: 1,105; COMMENTS: Different from A137979: first time these sequence disagree is at n=14235 with a(14235)=2 and A137979(14235)=3.; LINKS: Max Alekseyev, Table of n, a(n) for n = 1..100000 Alexandre Kosyak, Pieter Moree, Efthymios Sofos and Bin Zhang, Cyclotomic polynomials with prescribed height and prime number theory, arXiv:1910.01039 , 2019.### A005845 - OEIS

OFFSET: 1,1; COMMENTS: This uses the definition of "Lucas pseudoprime" by Bruckman, not the one by Baillie and Wagstaff. - R.J. Mathar, Jul 15 2012. Unlike the earlier Baillie-Wagstaff Lucas pseudoprimes A217120, these have significant overlap with the Fermat primality test.For example, the number 82380774001 is both an A005845 Lucas pseudoprime and a Fermat pseudoprime to the first 407### A247698 - OEIS

OFFSET: 1,1; COMMENTS: B(n) / B(n - 1) approaches the golden ratio as n approaches infinity. LINKS: Logan Cooper, Table of n, a(n) for n = 1..1000 (truncated from 9966 to 1000 terms by M. F. Hasler, May 10 2017) Brady Haran and Matt Parker, Brady Numbers, Numberphile video (2014) Index entries for linear recurrences with constant coefficients, signature (1,1).### A038445 - OEIS

The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.### A344937 - OEIS

A344937 a(n) is the largest k such that when strings of zeros of lengths t = 1..k are inserted between every pair of adjacent digits of prime(n), the resulting numbers are all primes.### A250001 - OEIS

OFFSET: 0,3; COMMENTS: Two circles are either disjoint or meet in two points. Tangential contacts are not allowed. A point belongs to exactly one or two circles.### A006881 - OEIS

A006881 Squarefree semiprimes: Numbers that are the product of two### distinct primes.

### A000254 - OEIS

A000254 Unsigned Stirling numbers of first kind, s(n+1,2): a(n+1) =### (n+1)*a(n) + n!.

### A344674 - OEIS

A344674 a(n) is the maximum value such that there is an n X n binary orthogonal matrix with every row having at least a(n) ones. LIST OF PRIME CONJECTURES This page was created to organize all the conjectures and unsolved problems involving prime numbers, listed from highest to least importance. If new, relevant conjectures are made, they may be added### to this page.

### A172132 - OEIS

0, 6, 28, 96, 252, 550, 1056, 1848, 3016, 4662, 6900, 9856, 13668, 18486, 24472, 31800, 40656, 51238, 63756, 78432, 95500, 115206, 137808, 163576, 192792, 225750### A342027 - OEIS

The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.### A344671 - OEIS

A344671 a(n) is the total number of stable matchings for all possible preference profiles in the stable marriage problem with n men and n women such that there exists a married couple where the woman and the man rank each other last.### A305805 - OEIS

The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. THE ON-LINE ENCYCLOPEDIA OF INTEGER SEQUENCES® (OEIS®)A005150STYLE SHEETSUPERSEEKERA000040MUSICA001220 The On-Line Encyclopedia of Integer Sequences® (OEIS®) For more information about the Encyclopedia, see the Welcome page. Languages: English Shqip العربية Bangla Български Català 中文 ( 正體字 , 简化字 L'ENCYCLOPÉDIE EN LIGNE DES SUITES DE NOMBRES …TRANSLATE THIS PAGE The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. LIST OF LATEX MATHEMATICAL SYMBOLS Hyperbolic functions The abbreviations arcsinh, arccosh, etc., are commonly used for inverse hyperbolic trigonometric functions (area hyperbolic functions), even though they are misnomers, since the prefix arc is the abbreviation for arcus, while the prefix ar stands### for area.

TOOTHPICK-LIKE SEQUENCE EXPLORATION Instructions See the OEIS entries for A139250, A147562, A151723, A151725, A160120, A161644, and A160720 for a description of the toothpick sequence and some other related sequences, and some background. Select a sequence, enter a value of N and click Update to draw the figure after N iterations.. Type selects the type of figure### drawn.

### A000010 - OEIS

A000010 Euler totient function phi(n): count numbers# Details

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