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 A182155 #16 Mar 06 2016 12:33:08
%S A182155 0,1,2,6,14,26,66,94,147,264,663,759,916,1089,1213,1343,1554,1706,
%T A182155 2113,2473,2661,2861,3069,3285,3513,3747,3989,4497,4763,5039,5323,
%U A182155 5911,6217,6527,6849,7179,7690,8227,8790,9566,9966,10995,11423,12076,12974,13438
%N A182155 Integers of the form: 0/3 + 1/3 + 2/3 + 3/3 + 5/3 + 7/3 + 11/3 + 13/3 + 17/3 + ....
%C A182155 Numbers k such that the sum of first n nonnegative noncomposite numbers is equal to 3k.
%H A182155 Harvey P. Dale, <a href="/A182155/b182155.txt">Table of n, a(n) for n = 1..1000</a>
%e A182155 1/3 + 2/3 = 1, 1/3 + 2/3 + 3/3 = 2, 1/3 + 2/3 + 3/3 + 5/3 + 7/3 = 6.
%t A182155 s = 1; t = {0}; Do[s = s + Prime[n]; If[Mod[s, 3] == 0, AppendTo[t, s/3]], {n, 200}]; t (* _T. D. Noe_, Apr 18 2012 *)
%t A182155 Select[Accumulate[Join[{0,1/3},Prime[Range[200]]/3]],IntegerQ] (* _Harvey P. Dale_, Mar 06 2016 *)
%Y A182155 Cf. A007504, A154293, A158611.
%K A182155 nonn
%O A182155 1,3
%A A182155 _Gerasimov Sergey_, Apr 15 2012
%E A182155 Definition corrected by _Harvey P. Dale_, Mar 06 2016