A141100 Number of unordered pairs of odd composite numbers that sum to 2n.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 1, 3, 1, 1, 3, 2, 1, 4, 1, 2, 5, 1, 3, 5, 1, 4, 5, 3, 3, 6, 3, 3, 7, 3, 3, 9, 3, 4, 7, 4, 6, 9, 5, 5, 8, 6, 6, 10, 5, 5, 12, 4, 6, 12, 5, 9, 11, 7, 7, 11, 9, 9, 13, 8, 8, 16, 7, 11, 14, 8, 11, 14, 9, 9, 17, 13, 10, 16, 11, 11, 19, 11, 12, 18, 10

Offset: 1

Author

T. D. Noe, Jun 02 2008, Jun 05 2008

Keywords

• nonn

Comments

See A141099 for pairs of odd nonprime numbers. We have a(n) > 0 except for the 14 values of 2n given in A118081.

Examples

			a(18)=2 because 36 = 9+27 = 15+21.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A005171, A118081, A141095, A141097, A141099.

Programs

Mathematica

Table[cnt=0; Do[If[ !PrimeQ[i] && !PrimeQ[2n-i], cnt++ ], {i,3,n,2}]; cnt, {n,100}]

Formula

a(n) = 1 - floor(n/2) + Sum_{i=3..n} c(i) * c(2n-i), n>1, where c = A005171. - Wesley Ivan Hurt, Dec 27 2013