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 A130216 #15 Jan 09 2015 20:23:45
%S A130216 3,4,5,6,8,10,12,15,19,23,27,32,37,42,48,55,62,69,77,85,93,102,112,
%T A130216 122,132,143,154,165,177,190,203,216,230,244,258,273,289,305,321,338,
%U A130216 355,372,390,409,428,447,467,487,507,528,550,572,594,617,640,663,687,712
%N A130216 a(0) = 3; a(n) = a(n-1) + (number of multiples of 3 so far in the sequence).
%C A130216 See A007980 for the same construction with multiples of 2.
%H A130216 Alois P. Heinz, <a href="/A130216/b130216.txt">Table of n, a(n) for n = 0..1000</a>
%F A130216 G.f.: -(3*x^8-2*x^7+x^4-2*x+3) / (x^9-2*x^8+x^7-x^2+2*x-1). - _Alois P. Heinz_, Aug 12 2009
%e A130216 3,4,5,6,8,10,12,15: next term is 19 which is 15 + 4 previous terms divisible by 3 (they are 3,6,12,15).
%p A130216 a:= proc(n) local m, r; m:= iquo(n, 7, 'r'); (3+21*m+6*r) *m/2 +[3, 4, 5, 6, 8, 10, 12][r+1] end: seq(a(n), n=0..80); # _Alois P. Heinz_, Aug 12 2009
%t A130216 l={3};Do[AppendTo[l,Last[l]+Count[l,_?(Divisible[#,3]&)]],{n,60}];l (* _Harvey P. Dale_, Jul 24 2011 *)
%K A130216 easy,nonn
%O A130216 0,1
%A A130216 _Eric Angelini_, Aug 05 2007
%E A130216 More terms from _Alois P. Heinz_, Aug 12 2009