A205617 - OEIS

%I #9 Mar 31 2012 10:28:36

%S 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,

%T 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,

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

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

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

%H Donovan Johnson, <a href="/A205617/b205617.txt">Table of n, a(n) for n = 1..10000</a>

%H J. Sondow, <a href="http://arxiv.org/abs/0907.5232"> Ramanujan primes and Bertrand's postulate</a>, Amer. Math. Monthly 116 (2009), 630-635.

%H J. Sondow, J. W. Nicholson, and T. D. Noe, <a href="http://arxiv.org/abs/1105.2249"> Ramanujan Primes: Bounds, Runs, Twins, and Gaps</a>, J. Integer Seq. 14 (2011) Article 11.6.2

%e 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.

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

%K nonn

%O 1,5

%A _John W. Nicholson_ and _Donovan Johnson_, Jan 30 2012