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

1,5

Comments

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

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

Example

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.

Crossrefs

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

Sequence in context: A117358 A294333 A321125 * A359888 A204112 A186027

Adjacent sequences: A205614 A205615 A205616 * A205618 A205619 A205620

Keyword

nonn

Author

John W. Nicholson and Donovan Johnson, Jan 30 2012

Status

approved