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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Aug 22 2015
STATUS
approved