cp's OEIS Frontend

A038601 Prime numbers p such that the number of partitions of p is also a prime.

%I A038601 #14 Jun 24 2025 13:27:43
%S A038601 2,3,5,13,157,491,863,1621,2633,5347,8117,13513,35227,62311,76367,
%T A038601 84017,141637,170537,189353,192667,201821,216617,251677,269257,288203,
%U A038601 293621,353807,366103,367621,372023,441703,444167,478571,518657,582371,626333,780707,816521
%N A038601 Prime numbers p such that the number of partitions of p is also a prime.
%H A038601 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha145.htm">Partition Number (n = 0 to 1000): Factorizations</a>.
%H A038601 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha146.htm">Partition Number (n = 1001 to 2000): Factorizations</a>.
%H A038601 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha147.htm">Partition Number (n = 2001 to 3000); Factorizations</a>.
%H A038601 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha148.htm">Partition Number (n = 3001 to 4000): Factorizations</a>.
%H A038601 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha149.htm">Partition Number (n = 4001 to 5000): Factorizations</a>.
%H A038601 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha150.htm">Partition Number (n = 5001 to 6000): Factorizations</a>.
%H A038601 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha151.htm">Partition Number (n = 6001 to 7000): Factorizations</a>.
%H A038601 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha152.htm">Partition Number (n = 7001 to 8000): Factorizations</a>.
%H A038601 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha153.htm">Partition Number (n = 8001 to 9000): Factorizations</a>.
%H A038601 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha154.htm">Partition Number (n = 9001 to 10000): Factorizations</a>.
%H A038601 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/part/index.htm">Factorization of Partition Number</a>.
%e A038601 5 = (1+1+1+1+1+1,1+1+1+2,1+1+3,1+4,1+2+2,2+3,5), so partition(5) = 7; 5 and 7 are primes.
%t A038601 Do[ If[ PrimeQ[n] && PrimeQ[ PartitionsP[n]], Print[n]], {n, 1, 10^5} ]
%Y A038601 Cf. A046063, A000041, A070177.
%K A038601 nonn
%O A038601 1,1
%A A038601 _Jeff Burch_
%E A038601 More terms from _Simon Plouffe_
%E A038601 More terms from _Robert G. Wilson v_, Aug 29 2001
%E A038601 a(17)-a(36) from _Jacques Tramu_, Jun 26 2005
%E A038601 Corrected by _T. D. Noe_, Oct 31 2006
%E A038601 Offset changed and a(37)-a(38) from _Michael S. Branicky_, Jun 24 2025