A224713 - OEIS

%I #11 May 01 2013 00:42:36

%S 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,

%T 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,

%U 19,6,23,20,10,24,17,13,21,22,16,19,19,12,23,24

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

%H J. Stauduhar, <a href="/A224713/b224713.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

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

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

%Y Subsequence of A224712.

%K nonn,easy

%O 1,6

%A _J. Stauduhar_, Apr 20 2013