A215461 Number of decompositions of 2n into ordered sums of one prime and one nonprime.
0, 0, 2, 2, 2, 0, 4, 4, 2, 4, 6, 4, 4, 6, 8, 6, 12, 6, 4, 16, 10, 8, 14, 12, 8, 12, 16, 10, 18, 16, 8, 24, 14, 10, 28, 16, 14, 22, 20, 12, 26, 24, 12, 26, 28, 10, 30, 28, 18, 36, 24, 18, 32, 30, 22, 32, 28, 18, 34, 36, 10, 44, 38, 18, 48, 32, 26, 40, 42, 32, 38, 36, 22, 44
Offset: 0
Keywords
Examples
n=15, 2*n=30, 2*n = { 3+27, 5+25, 29+1; 1+29, 25+5, 27+3 }, a(15) = 6
n=18, 2*n=36, 2*n = { 3+33, 11+25; 11+25, 33+3 }, a(18) = 4
Formula
a(n) = convolve(p,c) + convolve(c,p) = 2*convolve(p,c) where p(n) = 1 if 2n+1 is prime and 0 otherwise, and c(n) = 1 if 2n+1 is nonprime and 0 otherwise.
Comments