A205617 Number of decompositions of 2n into an unordered sum of two non-Ramanujan primes (A174635).

0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 3, 0, 1, 3, 1, 2, 2, 1, 3, 2, 0, 1, 3, 2, 1, 3, 1, 3, 4, 1, 2, 4, 1, 4, 2, 0, 3, 2, 3, 2, 3, 2, 3, 5, 1, 3, 4, 0, 5, 1, 0, 4, 3, 3, 1, 4, 3, 5, 4, 0, 4, 3, 1, 4, 2, 2, 6, 2, 3, 4, 4, 1, 3

Offset: 1

Author

John W. Nicholson and Donovan Johnson, Jan 30 2012

Keywords

• nonn

Comments

There are 15 zeros in the first 10^8 terms. a(n) > 0 for n from 315 to 10^8.

Examples

			a(25) = 3. 2*25 = 50 = 7+43 = 13+37 = 19+31 (7, 13, 19, 31, 37, and 43 are all non-Ramanujan primes (A174635)). 50 is the unordered sum of two non-Ramanujan primes in three ways.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000
• J. Sondow, Ramanujan primes and Bertrand's postulate, Amer. Math. Monthly 116 (2009), 630-635.
• J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, J. Integer Seq. 14 (2011) Article 11.6.2

Crossrefs

Cf. A104272, A174635, A173634, A204814, A205301, A205616, A205618.