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

Author

J. Stauduhar, Apr 20 2013

Keywords

• nonn
• easy

Examples

			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.
		

Links

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

Crossrefs

Subsequence of A224712.

Programs

PARI

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