OFFSET
1,1
COMMENTS
The conjecture in A259531 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) = 2 since p(1)^2 + p(1)^2 = 2 is prime.
a(2) = 5 since p(1)^2 + p(2)^2 = 1^2 + 2^2 = 5 is prime.
a(3) = 13 since p(2)^2 + p(3)^2 = 2^2 + 3^2 = 13 is prime.
a(4) = 29 since p(2)^2 + p(4)^2 = 2^2 + 5^2 = 29 is prime.
MATHEMATICA
n=0; Do[If[PrimeQ[PartitionsP[k]^2+PartitionsP[m]^2], n=n+1; Print[n, " ", PartitionsP[k]^2+PartitionsP[m]^2]], {m, 1, 34}, {k, 1, m}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jul 03 2015
STATUS
approved