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A261515
Primes of the form p(q) + p(r) with q and r both prime, where p(.) is the partition function given by A000041.
2
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, 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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Aug 22 2015
STATUS
approved