A215462 - OEIS

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

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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.