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 A047338 #15 Sep 08 2022 08:44:57
%S A047338 1,2,3,4,8,9,10,11,15,16,17,18,22,23,24,25,29,30,31,32,36,37,38,39,43,
%T A047338 44,45,46,50,51,52,53,57,58,59,60,64,65,66,67,71,72,73,74,78,79,80,81,
%U A047338 85,86,87,88,92,93,94,95,99,100,101,102,106,107,108,109
%N A047338 Numbers that are congruent to {1, 2, 3, 4} mod 7.
%H A047338 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047338 G.f.: x*(1+x+x^2+x^3+3*x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 2011
%F A047338 From _Wesley Ivan Hurt_, May 23 2016: (Start)
%F A047338 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047338 a(n) = (14n-15-3*i^(2n)-(3-3*i)*i^(-n)-(3+3*i)*i^n)/8 where i=sqrt(-1).
%F A047338 a(2n) = A047348(n), a(2n-1) = A047356(n). (End)
%F A047338 E.g.f.: (12 + 3*(sin(x) - cos(x)) + (7*x - 6)*sinh(x) + (7*x - 9)*cosh(x))/4. - _Ilya Gutkovskiy_, May 24 2016
%p A047338 A047338:=n->(14*n-15-3*I^(2*n)-(3-3*I)*I^(-n)-(3+3*I)*I^n)/8: seq(A047338(n), n=1..100); # _Wesley Ivan Hurt_, May 23 2016
%t A047338 Table[(14n-15-3*I^(2n)-(3-3*I)*I^(-n)-(3+3*I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, May 23 2016 *)
%o A047338 (Magma) [n : n in [0..150] | n mod 7 in [1, 2, 3, 4]]; // _Wesley Ivan Hurt_, May 23 2016
%Y A047338 Cf. A047348, A047356.
%K A047338 nonn,easy
%O A047338 1,2
%A A047338 _N. J. A. Sloane_
%E A047338 More terms from _Wesley Ivan Hurt_, May 23 2016