A261515 Primes of the form p(q) + p(r) with q and r both prime, where p(.) is the partition function given by A000041.

5, 17, 59, 71, 103, 157, 353, 787, 4567, 4621, 6857, 63317, 124769, 336773, 14178581, 37187119, 214544387, 214811057, 215602631, 271249247, 273928639, 431274143, 544625929, 851377883, 3913864351, 5964539507, 5964539519, 11097645023, 11097974947, 11102342221, 45063304271, 142799017567, 207890420203, 207913758571

Offset

1,1

Comments

The conjecture in A261513 implies that the current sequence has infinitely many terms.

References

Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28 - Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014.

Example

a(1) = 5 since p(2) + p(3) = 2 + 3 = 5 with 2, 3 and 5 all prime.
a(2) = 17 since p(2) + p(7) = 2 + 15 = 17 with 2, 7 and 17 all prime.

Mathematica

f[n_]:=PartitionsP[Prime[n]]
n=0; Do[If[PrimeQ[f[k]+f[m]], n=n+1; Print[n, " ", f[k]+f[m]]], {m, 1, 40}, {k, 1, m}]

Crossrefs

Cf. A000040, A000041, A259678, A261513.

Sequence in context: A009229 A010914 A180502 * A171838 A105392 A090857

Adjacent sequences: A261512 A261513 A261514 * A261516 A261517 A261518

Keyword

nonn

Author

Zhi-Wei Sun, Aug 22 2015

Status

approved