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

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

Cf. A000041, A035359, A049575, A051143, A111036, A111045, A114165, A111389, A113499, A114166, A114167, A114168, A114169, A114170, A115214.

Sequence in context: A200331 A010349 A032995 * A065638 A364224 A204896

Adjacent sequences: A046060 A046061 A046062 * A046064 A046065 A046066

Keyword

nonn,nice

Author

Eric W. Weisstein

Extensions

b-file extended by Max Alekseyev, Jul 07 2009, Jun 14 2011, Jan 08 2012, May 19 2014

Status

approved