A205618 -id:A205618 - cp's OEIS frontend

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

John W. Nicholson and Donovan Johnson, Jan 30 2012

nonn

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

			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.

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

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

A205616 Even numbers that are not the sum of two non-Ramanujan primes (A174635).

Original entry on oeis.org

2, 4, 52, 70, 100, 124, 130, 148, 208, 232, 238, 292, 352, 418, 628

Offset: 1

John W. Nicholson and Donovan Johnson, Jan 30 2012

nonn

No other terms < 2*10^8. Conjectured to be complete.

			70 is a term because no two non-Ramanujan primes (A174635) sum to 70. 72 is not a term because 19 + 53 = 72. 19 and 53 are both non-Ramanujan primes.

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

Cf. A104272, A174635, A173634, A204814, A205301, A205617, A205618.

cp's OEIS Frontend

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

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