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 A047564 #21 Sep 08 2022 08:44:57
%S A047564 1,3,4,5,6,7,9,11,12,13,14,15,17,19,20,21,22,23,25,27,28,29,30,31,33,
%T A047564 35,36,37,38,39,41,43,44,45,46,47,49,51,52,53,54,55,57,59,60,61,62,63,
%U A047564 65,67,68,69,70,71,73,75,76,77,78,79,81,83,84,85,86,87
%N A047564 Numbers that are congruent to {1, 3, 4, 5, 6, 7} mod 8.
%H A047564 Vincenzo Librandi, <a href="/A047564/b047564.txt">Table of n, a(n) for n = 1..1000</a>
%H A047564 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,2,-1).
%F A047564 From _Chai Wah Wu_, May 30 2016: (Start)
%F A047564 a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6) for n>6.
%F A047564 G.f.: x*(x^5 + x^3 + x + 1)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)). (End)
%F A047564 From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F A047564 a(n) = (12*n-3-sqrt(3)*(cos((1-4*n)*Pi/6)+3*cos((1+2*n)*Pi/6)))/9.
%F A047564 a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-5, a(6k-5) = 8k-7. (End)
%F A047564 Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)+1)*Pi/16 + sqrt(2)*log(sqrt(2)+2)/4 - (sqrt(2)+3)*log(2)/8. - _Amiram Eldar_, Dec 28 2021
%p A047564 A047564:=n->(12*n-3-sqrt(3)*(cos((1-4*n)*Pi/6)+3*cos((1+2*n)*Pi/6)))/9: seq(A047564(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t A047564 Select[Range[0, 100], MemberQ[{1, 3, 4, 5, 6, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 16 2016 *)
%t A047564 CoefficientList[Series[(x^5 + x^3 + x + 1) / ((x - 1)^2 (x^2 - x + 1) (x^2 + x + 1)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jun 18 2016 *)
%o A047564 (Magma) [n : n in [0..100] | n mod 8 in [1, 3, 4, 5, 6, 7]]; // _Wesley Ivan Hurt_, Jun 16 2016
%Y A047564 Cf. A047572, A047593.
%K A047564 nonn,easy
%O A047564 1,2
%A A047564 _N. J. A. Sloane_