This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A092464 #37 Nov 27 2024 07:26:56
%S A092464 4,9,17,22,30,35,43,48,56,61,69,74,82,87,95,100,108,113,121,126,134,
%T A092464 139,147,152,160,165,173,178,186,191,199,204,212,217,225,230,238,243,
%U A092464 251,256,264,269,277,282,290,295,303,308,316,321,329,334,342,347,355,360
%N A092464 Numbers congruent to 4 or 9 mod 13.
%C A092464 Numbers k such that k^2 is congruent to 3 (modulo 13).
%H A092464 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A092464 From _R. J. Mathar_, Apr 20 2009: (Start)
%F A092464 a(n) = a(n-2) + 13 = a(n-1) + a(n-2) - a(n-3) = 13*n/2 - 13/4 - 3*(-1)^n/4.
%F A092464 G.f.: x*(4+5*x+4*x^2)/((1+x)*(x-1)^2). (End)
%F A092464 a(n) = 13*(n-1) - a(n-1), (with a(1)=4). - _Vincenzo Librandi_, Nov 17 2010
%F A092464 Sum_{n>=1} (-1)^(n+1)/a(n) = tan(5*Pi/26)*Pi/13. - _Amiram Eldar_, Feb 27 2023
%F A092464 From _Amiram Eldar_, Nov 25 2024: (Start)
%F A092464 Product_{n>=1} (1 - (-1)^n/a(n)) = 2*sin(5*Pi/26).
%F A092464 Product_{n>=1} (1 + (-1)^n/a(n)) = sin(3*Pi/13)*sec(5*Pi/26). (End)
%t A092464 Select[Range[400],MemberQ[{4,9},Mod[#,13]]&] (* or *) Select[Range[400], PowerMod[#,2,13]==3&] (* _Harvey P. Dale_, Mar 05 2012 *)
%Y A092464 A127547 is a subsequence.
%K A092464 nonn,easy
%O A092464 1,1
%A A092464 Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Mar 25 2004
%E A092464 More terms from _Ray Chandler_, Mar 27 2004
%E A092464 Edited by _N. J. A. Sloane_, May 10 2007
%E A092464 Incorrect formula deleted by _N. J. A. Sloane_, Jun 16 2010