A046063 - OEIS

A046063

Numbers k such that the k-th partition number A000041(k) is prime.

2, 3, 4, 5, 6, 13, 36, 77, 132, 157, 168, 186, 188, 212, 216, 302, 366, 417, 440, 491, 498, 525, 546, 658, 735, 753, 825, 841, 863, 1085, 1086, 1296, 1477, 1578, 1586, 1621, 1793, 2051, 2136, 2493, 2502, 2508, 2568, 2633, 2727, 2732, 2871, 2912, 3027, 3098, 3168, 3342, 3542, 3641, 4118

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The corresponding primes are given in A049575. - Joerg Arndt, May 09 2013

LINKS

Max Alekseyev, Table of n, a(n) for n = 1..4967 (contains all terms below 10^8)

Chris K. Caldwell, Top twenty prime partition numbers, The Prime Pages.

G. P. Michon, Table of partition function p(n) (n=0 through 4096)

G. K. Patil, Ramanujan's Life And His Contributions In The Field Of Mathematics, International Journal of Scientific Research and Engineering Studies (IJSRES), Volume 1(6) (2014), ISSN: 2349-8862.

Eric Weisstein's World of Mathematics, Partition Function P Congruences.

Eric Weisstein's World of Mathematics, Partition Function P.

Eric Weisstein's World of Mathematics, Integer Sequence Primes.

MATHEMATICA

Select[ Range@3341, PrimeQ@ PartitionsP@# &] (* Robert G. Wilson v *)

PROG

(PARI) for(n=0, 10^5, my(p=numbpart(n)); if(isprime(p), print1(n, ", "))); \\ Joerg Arndt, May 09 2013

(Python)

from sympy import isprime, npartitions

print([n for n in range(1, 5001) if isprime(npartitions(n))]) # Indranil Ghosh, Apr 10 2017

CROSSREFS