A144466 Primes p such that the partition number of the p-th prime is also a prime.

2, 3, 37, 257, 1021, 1601, 67757, 193873, 331889, 332099, 843181, 1278029, 1437133, 1613153, 2160797, 2423873, 3076313, 3506039, 4108889, 4430753, 4656089, 5724349, 6206119, 7457503, 7487759, 7798649, 7978849, 8794811, 9036997, 11846183, 13075709, 13458323, 14773721, 15227543

Offset: 1

Author

Roger L. Bagula, Oct 09 2008

Keywords

• nonn

Examples

			37 is in the sequence because the 37th prime is 157, the partition number of 157 is 80630964769 and 80630964769 is a prime.
		

Crossrefs

Cf. A038601.

Programs

Mathematica

Flatten[Table[If[PrimeQ[PartitionsP[Prime[Prime[n]]]], Prime[n], {}], {n, 1, 2000}]]
Select[Prime[Range[260]],PrimeQ[PartitionsP[Prime[#]]]&] (* Harvey P. Dale, Nov 01 2011 *)

Formula

{ p in {A000040} : A000041(A000040(p)) in {A000040} }.

Extensions

Edited by Alois P. Heinz, Oct 26 2011

a(7)-a(21) from Michael S. Branicky, Sep 30 2023

a(22) and beyond from Michael S. Branicky, Jun 25 2025