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A235613 Number of ways to write n = k + m (0 < k <= m) with k and m terms of A235592.

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