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 A047499 #20 May 16 2025 18:23:59
%S A047499 3,4,5,7,11,12,13,15,19,20,21,23,27,28,29,31,35,36,37,39,43,44,45,47,
%T A047499 51,52,53,55,59,60,61,63,67,68,69,71,75,76,77,79,83,84,85,87,91,92,93,
%U A047499 95,99,100,101,103,107,108,109,111,115,116,117,119,123,124
%N A047499 Numbers that are congruent to {3, 4, 5, 7} mod 8.
%H A047499 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047499 G.f.: x*(3+x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Nov 06 2015
%F A047499 From _Wesley Ivan Hurt_, May 27 2016: (Start)
%F A047499 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047499 a(n) = (8*n-1-i^(2*n)-(1-2*i)*i^(-n)-(1+2*i)*i^n)/4 where i=sqrt(-1).
%F A047499 a(2k) = A047535(k), a(2k-1) = A047621(k). (End)
%F A047499 E.g.f.: 1 + sin(x) - cos(x)/2 + 2*x*sinh(x) + (2*x - 1/2)*cosh(x). - _Ilya Gutkovskiy_, May 27 2016
%F A047499 Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 + (4-3*sqrt(2))*log(2)/16 + 3*sqrt(2)*log(2-sqrt(2))/8. - _Amiram Eldar_, Dec 26 2021
%p A047499 A047499:=n->(8*n-1-I^(2*n)-(1-2*I)*I^(-n)-(1+2*I)*I^n)/4: seq(A047499(n), n=1..100); # _Wesley Ivan Hurt_, May 27 2016
%t A047499 Table[(8n-1-I^(2n)-(1-2*I)*I^(-n)-(1+2*I)*I^n)/4, {n, 80}] (* _Wesley Ivan Hurt_, May 27 2016 *)
%t A047499 LinearRecurrence[{1,0,0,1,-1},{3,4,5,7,11},70] (* _Harvey P. Dale_, May 16 2025 *)
%o A047499 (Magma) [n : n in [0..150] | n mod 8 in [3, 4, 5, 7]]; // _Wesley Ivan Hurt_, May 27 2016
%Y A047499 Cf. A047535, A047621.
%K A047499 nonn,easy
%O A047499 1,1
%A A047499 _N. J. A. Sloane_