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

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.

Sequence in context: A055894 A350226 A362136 * A357427 A168557 A328204

Adjacent sequences: A224710 A224711 A224712 * A224714 A224715 A224716

Keyword

nonn,easy

Author

J. Stauduhar, Apr 20 2013

Status

approved