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 A047313 #31 Sep 08 2022 08:44:56
%S A047313 1,4,5,6,8,11,12,13,15,18,19,20,22,25,26,27,29,32,33,34,36,39,40,41,
%T A047313 43,46,47,48,50,53,54,55,57,60,61,62,64,67,68,69,71,74,75,76,78,81,82,
%U A047313 83,85,88,89,90,92,95,96,97,99,102,103,104,106,109,110,111
%N A047313 Numbers that are congruent to {1, 4, 5, 6} mod 7.
%H A047313 Vincenzo Librandi, <a href="/A047313/b047313.txt">Table of n, a(n) for n = 1..1000</a>
%H A047313 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047313 G.f.: x*(1+3*x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Dec 03 2011
%F A047313 From _Wesley Ivan Hurt_, May 23 2016: (Start)
%F A047313 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047313 a(n) = (14n-3+i^(2n)-(3+i)*i^(-n)-(3-i)*i^n)/8 where i=sqrt(-1).
%F A047313 a(2n) = A047288(n), a(2n-1) = A047383(n). (End)
%F A047313 E.g.f.: (4 - sin(x) - 3*cos(x) + (7*x - 2)*sinh(x) + (7*x - 1)*cosh(x))/4. - _Ilya Gutkovskiy_, May 24 2016
%p A047313 A047313:= n-> iquo(n-1, 4, 'r')*7 +[1, 4, 5, 6][r+1]: seq(A047313(n), n=1..80); # _Alois P. Heinz_, Dec 04 2011
%t A047313 Select[Range[100],MemberQ[{1,4,5,6},Mod[#,7]]&] (* _Harvey P. Dale_, Apr 17 2011 *)
%t A047313 LinearRecurrence[{1, 0, 0, 1, -1}, {1, 4, 5, 6, 8}, 80] (* _Jean-François Alcover_, Feb 18 2016 *)
%o A047313 (Magma) [n : n in [0..150] | n mod 7 in [1, 4, 5, 6]]; // _Wesley Ivan Hurt_, May 23 2016
%Y A047313 Cf. A047288, A047383.
%K A047313 nonn,easy
%O A047313 1,2
%A A047313 _N. J. A. Sloane_