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Primes p such that the partition number of the p-th prime is also a prime.
0

%I #19 Sep 30 2023 21:41:51

%S 2,3,37,257,1021,1601,67757,193873,331889,332099,843181,1278029,

%T 1437133,1613153,2160797,2423873,3076313,3506039,4108889,4430753,

%U 4656089

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

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

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

%t Flatten[Table[If[PrimeQ[PartitionsP[Prime[Prime[n]]]], Prime[n], {}], {n, 1, 2000}]]

%t Select[Prime[Range[260]],PrimeQ[PartitionsP[Prime[#]]]&] (* _Harvey P. Dale_, Nov 01 2011 *)

%Y Cf. A038601.

%K nonn,more

%O 1,1

%A _Roger L. Bagula_, Oct 09 2008

%E Edited by _Alois P. Heinz_, Oct 26 2011

%E a(7)-a(21) from _Michael S. Branicky_, Sep 30 2023