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%I #8 Mar 30 2012 17:26:31
%S 0,0,0,0,0,0,0,1,0,1,1,1,1,1,2,2,2,2,2,2,2,2,1,2,3,3,3,3,2,3,3,3,3,3,
%T 3,4,4,4,3,3,3,4,4,4,4,5,4,4,4,4,5,4,5,5,5,5,5,4,5,6,5,6,6,6,6,6,6,6,
%U 7,6,6,6,6,7,6,7,7,7,7,7,7,6,7,8,7,7,7,7,8,8,7,8,8,8,9,8,8,9,8,8,8,8,9,9,8,9,9,9,8,9,9,9,9,10
%N Number m of ways of representing 2n+1 as a sum of three primes such that all 3m primes are distinct.
%C a(n) <= A102605(n) (Number of ways of writing 2n+1 as p+q+r where p,q,r are distinct primes).
%C Minimal numbers with n representation as sum of triple of primes such that all 3n primes are distinct are:
%C 15,29,49,71,91,119,137,167,189,227,
%C 255,273,317,345,375,369,435,483,495,535,
%C 567,597,641,651,699,731,755,791,821,867,921,975.
%e First number with m=1 is 15=3+5+7; for m=2,3,4 we have:
%e m=2: 29=3+7+19=5+11+13; m=3: 49=3+5+41=5+7+37=13+17+19; m=4: 71=3+7+61=5+13+53=7+11+53=13+17+41.
%Y Cf. A102605.
%K nonn
%O 0,15
%A _Zak Seidov_, Dec 01 2010
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