A215462 Number of decompositions of 2n into ordered sums of two odd nonprimes.

0, 1, 0, 0, 0, 2, 0, 0, 2, 1, 0, 2, 2, 2, 2, 3, 0, 4, 6, 0, 4, 5, 2, 4, 6, 5, 4, 7, 4, 6, 10, 2, 8, 11, 2, 9, 10, 6, 8, 13, 6, 8, 14, 8, 8, 17, 8, 10, 16, 7, 14, 17, 10, 12, 16, 11, 14, 19, 12, 12, 26, 10, 14, 25, 10, 19, 22, 16, 16, 21, 18, 20, 28, 18, 18, 31, 14, 23, 30, 16

Offset

0,6

Comments

A002372(n) + A215461(n) + a(n) = n.

Note: if n is odd-composite then a(n) is odd, otherwise even.

Conjecture: a(n) is never zero for n > 19, verified to 10^9.

Conjecture: a(n) > A215461(n) > A002372(n) for sufficiently large n.

Links

Table of n, a(n) for n=0..79.

Formula

a(n) = convolve(c,c) where c(n) is the sequence defined by 1 if (2*n+1) is odd nonprime (includes 1), and 0 if (2*n+1) is odd prime.

Example

n=15, 2*n=30, 2*n = { 9+21, 15+15, 21+9 }, a(15) = 3.
n=18, 2*n=36, 2*n = { 1+35, 9+27, 15+21, 21+15, 27+9, 35+1 }, a(18) = 6.

Crossrefs

Cf. A002372, A215461.

Sequence in context: A353428 A244738 A331195 * A025843 A303906 A178580

Adjacent sequences: A215459 A215460 A215461 * A215463 A215464 A215465

Keyword

nonn

Author

Peter A. Lawrence, Aug 11 2012

Status

approved