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 A047572 #16 Sep 08 2022 08:44:57
%S A047572 1,2,4,5,6,7,9,10,12,13,14,15,17,18,20,21,22,23,25,26,28,29,30,31,33,
%T A047572 34,36,37,38,39,41,42,44,45,46,47,49,50,52,53,54,55,57,58,60,61,62,63,
%U A047572 65,66,68,69,70,71,73,74,76,77,78,79,81,82,84,85,86,87
%N A047572 Numbers that are congruent to {1, 2, 4, 5, 6, 7} mod 8.
%H A047572 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A047572 From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F A047572 G.f.: x*(1+x+2*x^2+x^3+x^4+x^5+x^6) / ((x-1)^2*(1+x+x^2+x^3+x^4+x^5)).
%F A047572 a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
%F A047572 a(n) = (24*n-9-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18.
%F A047572 a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-6, a(6k-5) = 8k-7. (End)
%F A047572 Sum_{n>=1} (-1)^(n+1)/a(n) = (3*sqrt(2)-1)*Pi/16 + sqrt(2)*log(sqrt(2)+2)/8 - (sqrt(2)+4)*log(2)/16. - _Amiram Eldar_, Dec 28 2021
%p A047572 A047572:=n->(24*n-9-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047572(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t A047572 Select[Range[0, 100], MemberQ[{1, 2, 4, 5, 6, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 16 2016 *)
%o A047572 (PARI) a(n)=n\6*8+[-1,1,2,4,5,6][n%6+1] \\ _Charles R Greathouse IV_, Feb 24 2015
%o A047572 (Magma) [n : n in [0..100] | n mod 8 in [1, 2, 4, 5, 6, 7]]; // _Wesley Ivan Hurt_, Jun 16 2016
%Y A047572 Cf. A047422, A047504, A047519.
%K A047572 nonn,easy
%O A047572 1,2
%A A047572 _N. J. A. Sloane_