%I #92 Apr 03 2023 10:36:09

%S 2,3,4,5,6,13,36,77,132,157,168,186,188,212,216,302,366,417,440,491,

%T 498,525,546,658,735,753,825,841,863,1085,1086,1296,1477,1578,1586,

%U 1621,1793,2051,2136,2493,2502,2508,2568,2633,2727,2732,2871,2912,3027,3098,3168,3342,3542,3641,4118

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

%C The corresponding primes are given in A049575. - _Joerg Arndt_, May 09 2013

%H Max Alekseyev, <a href="/A046063/b046063.txt">Table of n, a(n) for n = 1..4967</a> (contains all terms below 10^8)

%H Chris K. Caldwell, <a href="https://t5k.org/top20/page.php?id=54">Top twenty prime partition numbers</a>, The Prime Pages.

%H G. P. Michon, <a href="http://www.numericana.com/data/partition.htm">Table of partition function p(n) (n=0 through 4096)</a>

%H G. K. Patil, <a href="https://web.archive.org/web/20150911053452/http://www.ijsres.com/2014/vol-1_issue-6/paper_8.pdf">Ramanujan's Life And His Contributions In The Field Of Mathematics</a>, International Journal of Scientific Research and Engineering Studies (IJSRES), Volume 1(6) (2014), ISSN: 2349-8862.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionPCongruences.html">Partition Function P Congruences</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>.

%t Select[ Range@3341, PrimeQ@ PartitionsP@# &] (* _Robert G. Wilson v_ *)

%o (PARI) for(n=0,10^5,my(p=numbpart(n));if(isprime(p),print1(n,", "))); \\ _Joerg Arndt_, May 09 2013

%o (Python)

%o from sympy import isprime, npartitions

%o print([n for n in range(1, 5001) if isprime(npartitions(n))]) # _Indranil Ghosh_, Apr 10 2017

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

%K nonn,nice

%O 1,1

%A _Eric W. Weisstein_

%E b-file extended by _Max Alekseyev_, Jul 07 2009, Jun 14 2011, Jan 08 2012, May 19 2014