A205616 -id:A205616 - 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.

A205618 Last occurrence of n partitions in A205617.

Original entry on oeis.org

314, 629, 959, 1154, 1424, 4619, 1922, 4094, 2549, 3884, 3989, 5774, 4724, 5669, 6404, 5879, 7664, 5594, 8609, 9239, 9029, 8714, 10562, 10394, 9869, 11549, 9764, 12239, 11444, 11969, 11654, 14279, 14489, 12209, 13229, 15014, 13859, 14804, 15584, 16979, 19634

Offset: 0

John W. Nicholson and Donovan Johnson, Jan 30 2012

nonn

			a(0) = 314 because the last occurrence of a zero in A205617 is at a(314).

Donovan Johnson, Table of n, a(n) for n = 0..1000
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, A205617.

cp's OEIS Frontend

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

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