A009005 - OEIS

%I #33 Dec 02 2024 16:29:05

%S 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,

%T 29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,

%U 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

%N All natural numbers except 1, 2 and 4.

%C Short legs of Pythagorean triangles.

%C 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

%C 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

%C 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

%C 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

%H IBM Ponder This, <a href="https://research.ibm.com/haifa/ponderthis/challenges/December2001.html">December 2001</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

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

%t Join[{3}, Range[5, 100]] (* _Paolo Xausa_, Sep 13 2024 *)

%o (PARI) a(n)=n+4-(n==1) \\ _Charles R Greathouse IV_, Sep 02 2011

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

%K nonn,easy

%O 1,1

%A _David W. Wilson_