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 A047487 #31 Sep 08 2022 08:44:57
%S A047487 2,3,5,7,10,11,13,15,18,19,21,23,26,27,29,31,34,35,37,39,42,43,45,47,
%T A047487 50,51,53,55,58,59,61,63,66,67,69,71,74,75,77,79,82,83,85,87,90,91,93,
%U A047487 95,98,99,101,103,106,107,109,111,114,115,117,119,122,123
%N A047487 Numbers that are congruent to {2, 3, 5, 7} mod 8.
%H A047487 Vincenzo Librandi, <a href="/A047487/b047487.txt">Table of n, a(n) for n = 1..1000</a>
%H A047487 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047487 From _Colin Barker_, May 14 2012: (Start)
%F A047487 a(n) = (-3-(-1)^n+i*(-i)^n-i*i^n+8*n)/4 where i=sqrt(-1).
%F A047487 G.f.: x*(2+x+2*x^2+2*x^3+x^4)/((1-x)^2*(1+x)*(1+x^2)). (End)
%F A047487 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - _Vincenzo Librandi_, May 17 2012
%F A047487 a(2k) = A004767(k-1) for n>0, a(2k-1) = A047617(k). - _Wesley Ivan Hurt_, Jun 01 2016
%F A047487 E.g.f.: (2 + sin(x) + (4*x - 1)*sinh(x) + (4*x - 2)*cosh(x))/2. - _Ilya Gutkovskiy_, Jun 02 2016
%F A047487 Sum_{n>=1} (-1)^(n+1)/a(n) = (4-sqrt(2))*Pi/16 - log(2)/8 + sqrt(2)*log(sqrt(2)-1)/8. - _Amiram Eldar_, Dec 25 2021
%p A047487 A047487:=n->(-3-(-1)^n+I*(-I)^n-I*I^n+8*n)/4: seq(A047487(n), n=1..100); # _Wesley Ivan Hurt_, Jun 01 2016
%t A047487 Select[Range[0,300], MemberQ[{2,3,5,7}, Mod[#,8]]&] (* _Vincenzo Librandi_, May 17 2012 *)
%o A047487 (Magma) I:=[2, 3, 5, 7, 10]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // _Vincenzo Librandi_, May 17 2012
%o A047487 (PARI) my(x='x+O('x^100)); Vec(x*(2+x+2*x^2+2*x^3+x^4)/((1-x)^2*(1+x)*(1+x^2))) \\ _Altug Alkan_, Dec 24 2015
%Y A047487 Cf. A004767, A047617.
%K A047487 nonn,easy
%O A047487 1,1
%A A047487 _N. J. A. Sloane_