A229492 Conjectured number of positive even numbers having exactly n representations as the unordered sum of two odd primes.

2, 3, 9, 11, 11, 16, 16, 18, 20, 23, 16, 29, 16, 25, 27, 23, 22, 25, 35, 29, 26, 25, 27, 27, 27, 33, 28, 44, 35, 21, 29, 35, 38, 33, 39, 37, 34, 35, 31, 31, 28, 41, 37, 32, 44, 35, 37, 41, 44, 33, 37, 32, 47, 39, 43, 47, 33, 37, 48, 41, 37, 48, 34, 35, 47, 36, 29

Offset: 0

Author

T. D. Noe, Oct 31 2013

Keywords

• nonn

Comments

This sequence is closely related to the Goldbach conjecture, which is equivalent to a(0) = 2; that is, there are no numbers other than 2 and 4 that have no representations as the sum of two odd primes. This is sequence A000974, except for the first two terms.

Examples

			There are 3 even numbers with one representation: 6 = 3+3, 8 = 3+5, and 12 = 5+7. Hence, a(1) = 3.
		

Crossrefs

Cf. A000974 (using both even and odd primes).

Cf. A002375 (number of representations of 2n as the sum of two odd primes).