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%I #17 Mar 10 2014 05:09:40
%S 1,1,2,2,3,3,3,2,3,3,3,3,4,4,3,3,4,4,3,3,5,4,4,4,5,4,4,3,4,6,4,3,7,4,
%T 3,5,6,5,5,5,6,7,4,4,9,5,5,7,6,5,5,4,5,7,4,3,10,4,4,8,8,7,7,5,6,8,5,4,
%U 10,5,5,9,8,7,8,5,7,9,5,4,13,8,6,8,8,7
%N The number of unordered ways that n can be written as the sum of two numbers of the form p or 2p, where p is prime.
%C p and 2p are terms of A001751.
%C Sequence defined for n >= 4.
%C It is conjectured that all terms of this sequence are greater than zero.
%H Lei Zhou, <a href="/A238268/b238268.txt">Table of n, a(n) for n = 4..10000</a>
%e n=4, 4=2+2, one case found. So a(4)=1;
%e ...
%e n=24, 24 = 2+2*11 = 5+19 = 7+17 = 2*5+2*7 = 11+13, 5 cases found. So a(24)=5;
%e ...
%e n=33, 33 = 2+31 = 2*2+29 = 7+2*13 = 2*5+23 = 11+2*11 = 2*7+19, 6 cases found. So a(33)=6.
%t Table[ct = 0; Do[If[((PrimeQ[i]) || (PrimeQ[i/2])) && ((PrimeQ[n - i]) || (PrimeQ[(n - i)/2])), ct++], {i, 2, Floor[n/2]}]; ct, {n, 4, 89}]
%o (PARI) isp(i) = isprime(i) || (((i % 2) == 0) && isprime(i/2));
%o a(n) = sum(i=1, n\2, isp(i) && isp(n-i)); \\ _Michel Marcus_, Mar 07 2014
%Y Cf. A001751, A002375, A103151.
%K nonn
%O 4,3
%A _Lei Zhou_, Feb 21 2014
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