%I #8 Jan 13 2014 01:11:43
%S 0,0,0,1,1,2,2,3,2,3,3,3,3,3,2,3,4,3,3,4,3,5,6,5,4,4,3,4,6,5,4,5,4,4,
%T 5,4,4,6,5,8,6,6,5,5,6,6,8,6,6,6,4,7,6,5,7,9,6,6,8,5,4,7,9,7,8,6,6,7,
%U 3,5,7,9,8,9,9,6,6,5,6,7,6,8,5,4,4,4,4,8,10,10,10,7,6,6,8,7,6,10,6,6
%N Number of ways to write n = k + m (0 < k <= m) with k and m terms of A235592.
%C Conjecture: a(n) > 0 for all n > 3.
%H ZhiWei Sun, <a href="/A235613/b235613.txt">Table of n, a(n) for n = 1..10000</a>
%e a(4) = 1 since 4 = 2 + 2 with 2*(2+1)  prime(2) = 3 prime.
%e a(5) = 1 since 5 = 2 + 3 with 2*(2+1)  prime(2) = 3 and 3*(3+1)  prime(3) = 7 both prime.
%t p[n_]:=PrimeQ[n(n+1)Prime[n]]
%t a[n_]:=Sum[If[p[k]&&p[nk],1,0],{k,1,n/2}]
%t Table[a[n],{n,1,100}]
%Y Cf. A000040, A235592, A235614.
%K nonn
%O 1,6
%A _ZhiWei Sun_, Jan 12 2014
