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 A024684 #19 Jun 09 2014 12:50:02
%S A024684 0,0,0,0,0,0,0,1,2,3,4,5,6,6,9,11,13,13,15,18,17,19,25,26,28,32,31,37,
%T A024684 32,39,44,51,54,48,60,55,62,64,73,80,79,74,89,84,92,86,92,107,119,105,
%U A024684 118,122,117,135,143,146,147,141,149,159,157,176,175,190,180
%N A024684 Number of ways prime(n) is a sum of three distinct primes.
%H A024684 Zak Seidov and T. D. Noe, <a href="/A024684/b024684.txt">Table of n, a(n) for n = 1..10000</a> (first 2000 terms from Zak Seidov)
%H A024684 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach's_weak_conjecture">Goldbach's weak conjecture</a>
%F A024684 a(n) = A125688(prime(n)). - _R. J. Mathar_, Jun 09 2014
%e A024684 a(9) = 2 because prime(9) = 23 and 23 = 3 + 7 + 13 = 5 + 7 + 11.
%t A024684 last = 313; pp = PrimePi[last]; t = Select[Sort[Tally[Select[Total /@ Subsets[Prime[Range[2, pp]], {3}], PrimeQ]]], #[[1]] <= last &]; Join[{0, 0, 0, 0, 0, 0, 0}, Transpose[t][[2]]] (* _T. D. Noe_, Apr 15 2013 *)
%Y A024684 Cf. A002372, A002375, A224534.
%K A024684 nonn
%O A024684 1,9
%A A024684 _Clark Kimberling_