A009005 All natural numbers except 1, 2 and 4.

3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• easy

Comments

Short legs of Pythagorean triangles.

Also the natural numbers n such that there is an open knight's tour of the 4 X n chessboard. - Sharon Sela (sharonsela(AT)hotmail.com), Jan 02 2002

Also perimeters of integral triangles; equivalently, numbers n = a + b + c, where a + b > c, a + c > b, b + c > a, and a, b, c are integers (necessarily a, b, c, and n are positive). - Rick L. Shepherd, Aug 04 2013

Along with 0, possible scores in rugby union, where points can be scored with a penalty goal or drop goal (3 points), try (5 points) and converted try (7 points). - Charles R Greathouse IV, Sep 10 2016

Also the positive integers n such that floor(t(n+2)/(t(n+2) - sigma(n+2))) = 1, where t(n) = n*(n+1)/2 = A000217(n) and sigma(n) = A000203(n) (see A242963). - Lorenzo Sauras Altuzarra, Jan 29 2020

Links

• IBM Ponder This, December 2001
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A000203 (sigma function), A000217 (triangular numbers), A242963.

Programs

Mathematica

Join[{3}, Range[5, 100]] (* Paolo Xausa, Sep 13 2024 *)

PARI

a(n)=n+4-(n==1) \\ Charles R Greathouse IV, Sep 02 2011

Formula

O.g.f.: x(3-x-x^2)/(1-x)^2. a(n)=A009056(n), n>1. - R. J. Mathar, May 26 2008