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%I #6 May 09 2013 18:43:54
%S 0,0,0,0,0,0,0,0,0,1,1,1,0,2,2,1,1,2,1,1,1,2,2,3,0,1,3,1,2,3,2,3,1,2,
%T 3,2,1,2,3,1,1,3,2,3,1,2,3,3,2,4,2,2,2,4,2,3,3,2,4,3,2,4,3,3,4,2,2,3,
%U 2,2,4,3,2,5,3,2,4,5,3,4,2,4,5,4,2,4,3
%N Number of ways to express 2n+1 as p + 8*q, with p and q primes.
%C This is related to the conjecture given in A223174 and A223175.
%C For n > 8, a(12) = a(24) = 0 because A223174(12)= A223174(24)= 0.
%H Michel Lagneau, <a href="/A225518/b225518.txt">Table of n, a(n) for n = 0..10000</a>
%e a(14) = 2 because 29 = 5+8*3 = 13+8*2 with 2 decompositions.
%e a(23) = 3 because 47 = 7+8*5 = 23+8*3 = 31+8*2 with 3 decompositions.
%t a[n_] := (ways = 0; Do[p = 2k + 1; q = (n-k)/4; If[PrimeQ[p] && PrimeQ[q], ways++], {k, 1, n}]; ways); Table[a[n], {n, 0, 90}]
%Y Cf. A219254, A223174, A223175.
%K nonn
%O 0,14
%A _Michel Lagneau_, May 09 2013
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