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 A254680 #7 Feb 05 2015 09:38:13
%S A254680 1,3,7,17,21,51,66,72,157,147,121,136,246,297,332,367,402,506,547,577,
%T A254680 677,796,892,731,926,1216,1116,976,1181,1402,1556,1416,1507,1496,2287,
%U A254680 1622,1977,2112,1942,2131,2017,2882,2767,2501,3162,3671,3097,3187,3047,3762,3867,2952,4356,4111,4826,5112,5211,4811,4686,5461
%N A254680 Least positive integer m with A254661(m) = n.
%C A254680 Conjecture: a(n) exists for any n > 0. Moreover, no term is divisible by 5, and no term with n>2 is congruent to 3 modulo 5.
%H A254680 Zhi-Wei Sun, <a href="/A254680/b254680.txt">Table of n, a(n) for n = 1..170</a>
%H A254680 Zhi-Wei Sun, <a href="http://arxiv.org/abs/0905.0635">On universal sums of polygonal numbers</a>, arXiv:0905.0635 [math.NT], 2009-2015.
%p A254680 a(3) = 7 since 7 is the first positive integer that can be written as x*(x+1)/2 + (2y)^2 + z*(3*z+1)/2 (with x,y,z nonnegative integers) in exactly 3 ways. In fact, 7 = 0*1/2 + 0^2 +2*(3*2+1)/2 = 1*2/2 + 2^2 +1*(3*1+1)/2 = 2*3/2 + 2^2 + 0*(3*0+1)/2.
%t A254680 TQ[n_]:=IntegerQ[Sqrt[8n+1]]
%t A254680 Do[Do[m=0;Label[aa];m=m+1;r=0;Do[If[TQ[m-4y^2-z(3z+1)/2],r=r+1;If[r>n,Goto[aa]]],{y,0,Sqrt[m/4]}, {z,0,(Sqrt[24(m-4y^2)+1]-1)/6}];
%t A254680 If[r==n,Print[n," ",m];Goto[bb],Goto[aa]]]; Label[bb];Continue,{n,1,60}]
%Y A254680 Cf. A000217, A000290, A005449, A160325, A254661, A254677.
%K A254680 nonn
%O A254680 1,2
%A A254680 _Zhi-Wei Sun_, Feb 05 2015