Voozh

A224713

The number of unordered partitions {a, b} of the even numbers 2n such that a or b is composite and the other is prime.

0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 2, 4, 5, 3, 6, 4, 3, 8, 6, 4, 7, 7, 4, 7, 9, 5, 10, 9, 4, 12, 8, 6, 14, 9, 7, 11, 11, 7, 13, 13, 6, 14, 15, 5, 16, 15, 10, 18, 13, 9, 16, 16, 11, 16, 15, 9, 18, 19, 6, 23, 20, 10, 24, 17, 13, 21, 22, 16, 19, 19, 12, 23, 24

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OFFSET

1,6

LINKS

J. Stauduhar, Table of n, a(n) for n = 1..10000

EXAMPLE

For n = 3, 2n=6. In the set {{5, 1}, {4, 2}, {3, 3}}, {4, 2} is the only partition that satisfies the requirements, so a(3) = 1.

For n = 10, 2n=20 and we have partitions {18, 2}, {15, 5}, and {11, 9}, so a(10) = 3.

PROG

(PARI) a(n)=my(s); n*=2; forprime(p=2, n-4, s+=!isprime(n-p)); s \\ Charles R Greathouse IV, Apr 30 2013

CROSSREFS

Subsequence of A224712.