The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #6 Dec 25 2016 00:28:58
%S 1,6,9,15,17,21,27,33,39,41,45,47,51,53,57,63,65,71,77,83,89,95,101,
%T 107,113,119,125,131,137,143,149,155,161,167,173,185,191,197,203,209,
%U 215,221,227,233,239,245,251,257,269,275,277,281,287,293,299,305,311,317
%N Record values of n in A068307.
%H Robert G. Wilson v and T. D. Noe, <a href="/A139322/b139322.txt">Table of n, a(n) for n = 0..5000</a>
%t f[n_] := Block[{c = 0, lmt = PrimePi@ Floor[n/2], p, q}, Do[p = Prime@ i; q = Prime@ j; r = n - p - q; If[ PrimeQ@ r && r >= p, c++ ], {i, lmt}, {j, i}]; c]; lst = {1}; Do[ If[f@n > f@lst[[ -1]], AppendTo[lst, n]], {n, 13450}]; lst
%Y Cf. A000040, A068307, A139321.
%K nonn
%O 0,2
%A _Robert G. Wilson v_, Apr 13 2008