A188766 Numbers n such that the number of decompositions of 2n into sum of two primes (counting 1 as a prime) is 1 or a composite.

1, 12, 15, 17, 18, 22, 23, 24, 25, 27, 29, 31, 33, 37, 42, 44, 45, 46, 49, 50, 51, 52, 53, 54, 58, 59, 60, 61, 63, 64, 66, 67, 69, 70, 71, 73, 77, 79, 80, 81, 82, 83, 84, 85, 86, 87, 90, 92, 95, 96, 97, 98, 99, 100, 101, 102, 107, 110, 112, 115, 117, 118, 119

Offset: 1

Author

Jonathan Vos Post, Apr 09 2011

Keywords

• nonn
• easy

Comments

Arises in Goldbach conjecture.

Examples

			1 is a term because there is a unique decomposition of 2*1 = 2 into a sum of two primes (counting 1 as a prime), namely 2 = 1 + 1.
12 is a term because there are 4 decompositions of 2*12 = 24 into a sum of two primes (counting 1 as a prime), namely 1 + 23, 5 + 19, 7 + 17, and 11 + 13, and 4 is a composite number.
		

Crossrefs

Cf. A000040, A001031, A002808, A018252.

Programs

Sage

def is_A188766(n):
    pp = set(prime_range(2*n+1)+[1])
    return not is_prime(len([x for x in Partitions(2*n,length=2) if set(x) <= pp]))
# D. S. McNeil, Apr 10 2011

Formula

{integers n > 0 such that A001031(n) is in A018252} = {integers n > 0 such that A001031(n) is not in A000040}.