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 A047292 #37 Sep 08 2022 08:44:56
%S A047292 2,4,6,9,11,13,16,18,20,23,25,27,30,32,34,37,39,41,44,46,48,51,53,55,
%T A047292 58,60,62,65,67,69,72,74,76,79,81,83,86,88,90,93,95,97,100,102,104,
%U A047292 107,109,111,114,116,118,121,123,125,128,130,132,135,137,139,142,144
%N A047292 Numbers that are congruent to {2, 4, 6} mod 7.
%H A047292 Vincenzo Librandi, <a href="/A047292/b047292.txt">Table of n, a(n) for n = 1..5000</a>
%H A047292 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047292 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A047292 a(n) = floor((7*n-1)/3). [_Gary Detlefs_, May 14 2011]
%F A047292 G.f.: x*(2+2*x+2*x^2+x^3)/((1-x)^2*(1+x+x^2)). [_Colin Barker_, Mar 13 2012]
%F A047292 a(n) = 2*n + ceiling(n/3) - 1. - _Arkadiusz Wesolowski_, Sep 19 2012
%F A047292 From _Wesley Ivan Hurt_, Jun 10 2016: (Start)
%F A047292 a(n) = (21*n-6-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.
%F A047292 a(3k) = 7k-1, a(3k-1) = 7k-3, a(3k-2) = 7k-5. (End)
%p A047292 A047292:=n->(21*n-6-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047292(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016
%t A047292 Select[Range[0,125], MemberQ[{2,4,6}, Mod[#,7]]&] (* _Vincenzo Librandi_, Apr 26 2012 *)
%t A047292 LinearRecurrence[{1,0,1,-1},{2,4,6,9},70] (* _Harvey P. Dale_, Feb 06 2019 *)
%o A047292 (Magma) I:=[2, 4, 6, 9]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // _Vincenzo Librandi_, Apr 26 2012
%o A047292 (PARI) a(n) = 2*n + ceil(n/3) - 1; /* _Joerg Arndt_, Sep 20 2012 */
%K A047292 nonn,easy
%O A047292 1,1
%A A047292 _N. J. A. Sloane_