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 A109825 #3 Mar 30 2012 17:26:17
%S A109825 1,4,5,9,10,11,16,18,21,22,23,36,39,40,43,45,47,49,50,54,60,62,63,69,
%T A109825 70,72,74,75,89,93,94,95,96,99,104,106,107,109,111,112,115,116,126,
%U A109825 128,135,140,144,146,147,149,151,153,159,160,162,165,170,172,175,179,184,190
%N A109825 Initial terms of groups in the partition of the sequence of natural numbers A109411.
%t A109825 s={1};a=1;Do[Do[If[Plus@@Last/@FactorInteger[(a+x)(x-a+1)/2]==2, a=x+1;AppendTo[s, a];Break[]], {x, a, 20000}], {k, 1, 100}];A109825=s
%Y A109825 Cf. A109411, A109826.
%K A109825 nonn
%O A109825 1,2
%A A109825 _Zak Seidov_, Jul 03 2005