OFFSET
1,1
COMMENTS
Conjecture: a(n) exists for any n > 0.
This implies the conjecture that the sequence p(n) (n = 1,2,3,...) contains infinitely many primes.
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..88
Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014.
EXAMPLE
a(1) = 2 since p(2*1) = 2 is prime.
a(4) = 47 since 47 and p(47*4) = p(188) = 1398341745571 are both prime.
MATHEMATICA
Do[k=0; Label[bb]; k=k+1; If[PrimeQ[PartitionsP[Prime[k]*n]], Goto[aa], Goto[bb]]; Label[aa]; Print[n, " ", Prime[k]]; Continue, {n, 1, 50}]
PROG
(PARI) a(n)={my(r=1); while(!isprime(numbpart(prime(r)*n)), r++); return(prime(r)); }
main(size)={return(vector(size, n, a(n))); } /* Anders Hellström, Jul 12 2015 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jul 12 2015
STATUS
approved