A236418 Primes p with A047967(p) also prime.

13, 23, 43, 53, 71, 83, 107, 257, 269, 313, 1093, 2659, 2851, 3527, 8243, 20173, 20717, 24329, 26161, 26237, 31583, 53611, 60719, 74717, 83401, 118259, 118369, 130817, 133811, 145109, 152381, 169111, 178613, 183397, 205963

Offset: 1

Author

Zhi-Wei Sun, Jan 25 2014

Keywords

• nonn

Comments

According to the conjecture in A236417, this sequence should have infinitely many terms.

Examples

			a(1) = 13 with 13 and A047967(13) = 83 both prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..42

Crossrefs

Cf. A000040, A047967, A234530, A234569, A234644, A235344, A235346, A236413, A236417, A236419, A236440.

Programs

Mathematica

pq[n_]:=PrimeQ[n]&&PrimeQ[PartitionsP[n]-PartitionsQ[n]]
n=0;Do[If[pq[m],n=n+1;Print[n," ",m]],{m,1,10000}]
Select[Prime[Range[20000]],PrimeQ[PartitionsP[#]-PartitionsQ[#]]&] (* Harvey P. Dale, Jan 02 2022 *)