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

1,15

Comments

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

Links

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

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A238406 A058709 A025842 * A270655 A229140 A280317

Adjacent sequences: A141097 A141098 A141099 * A141101 A141102 A141103

Keyword

nonn,changed

Author

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

Status

approved