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 A047540 #21 Apr 29 2023 14:14:34
%S A047540 0,2,4,7,8,10,12,15,16,18,20,23,24,26,28,31,32,34,36,39,40,42,44,47,
%T A047540 48,50,52,55,56,58,60,63,64,66,68,71,72,74,76,79,80,82,84,87,88,90,92,
%U A047540 95,96,98,100,103,104,106,108,111,112,114,116,119,120,122,124
%N A047540 Numbers that are congruent to {0, 2, 4, 7} mod 8.
%C A047540 The products of an odd number of terms as well as products of one term each of this sequence and one term of A047409 are members. The products of an even number of terms belong to A047409. The union of this sequence and A047409 is closed under multiplication. - _Klaus Purath_, Apr 23 2023
%H A047540 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047540 From _Wesley Ivan Hurt_, May 29 2016: (Start)
%F A047540 G.f.: x^2*(2+2*x+3*x^2+x^3) / ((x-1)^2*(1+x+x^2+x^3)).
%F A047540 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047540 a(n) = (8*n-7+i^(2*n)+i^(-n)+i^n)/4 where i=sqrt(-1).
%F A047540 a(2k) = A047524(k), a(2k-1) = A008586(k-1) for k>0. (End)
%F A047540 Sum_{n>=2} (-1)^n/a(n) = (10-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8 - sqrt(2)*Pi/16. - _Amiram Eldar_, Dec 21 2021
%p A047540 A047540:=n->(8*n-7+I^(2*n)+I^(-n)+I^n)/4: seq(A047540(n), n=1..100); # _Wesley Ivan Hurt_, May 29 2016
%t A047540 Table[(8n-7+I^(2n)+I^(-n)+I^n)/4, {n, 80}] (* _Wesley Ivan Hurt_, May 29 2016 *)
%t A047540 {0,2,4,7}+#&/@(8*Range[0,20])//Flatten (* _Harvey P. Dale_, Dec 20 2022 *)
%o A047540 (Magma) [n : n in [0..150] | n mod 8 in [0, 2, 4, 7]]; // _Wesley Ivan Hurt_, May 29 2016
%Y A047540 Cf. A008586, A047524.
%K A047540 nonn,easy
%O A047540 1,2
%A A047540 _N. J. A. Sloane_