cp's OEIS Frontend

A236831 Number of ordered ways to write n = p + q with q > 0 such that p, p + 2 and p + prime(q) + 1 are all prime.

%I A236831 #16 Apr 06 2014 13:05:35
%S A236831 0,0,0,0,1,0,1,1,2,1,2,1,0,2,2,2,2,2,1,2,2,3,2,2,2,3,1,3,1,4,3,2,3,2,
%T A236831 3,2,3,1,2,2,4,3,1,3,3,3,3,3,4,2,4,4,4,3,2,2,3,4,3,4,4,2,3,4,5,3,2,6,
%U A236831 5,1,4,2,5,4,4,4,1,6,4,2,5,3,4,5,1,2,3,4,4,3,5,4,7,3,3,2,3,4,5,4
%N A236831 Number of ordered ways to write n = p + q with q > 0 such that p, p + 2 and p + prime(q) + 1 are all prime.
%C A236831 Conjecture: a(n) > 0 for all n > 13.
%H A236831 Zhi-Wei Sun, <a href="/A236831/b236831.txt">Table of n, a(n) for n = 1..10000</a>
%H A236831 Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014
%e A236831 a(12) = 1 since 12 = 5 + 7 with 5, 5 + 2 = 7 and 5 + prime(7) + 1 = 5 + 17 + 1 = 23 all prime.
%e A236831 a(85) = 1 since 85 = 29 + 56 with 29, 29 + 2 = 31 and 29 + prime(56) + 1 = 29 + 263 + 1 = 293 all prime.
%t A236831 p[n_,m_]:=PrimeQ[m+2]&&PrimeQ[m+Prime[n-m]+1]
%t A236831 a[n_]:=Sum[If[p[n,Prime[k]],1,0],{k,1,PrimePi[n-1]}]
%t A236831 Table[a[n],{n,1,100}]
%Y A236831 Cf. A000040, A001359, A006512, A236531.
%K A236831 nonn
%O A236831 1,9
%A A236831 _Zhi-Wei Sun_, Jan 31 2014