A242979 Primes p such that p^3-2 and p^2-2 are both primes.

19, 37, 211, 727, 2287, 4507, 4951, 5857, 6217, 6337, 7237, 8329, 8629, 8941, 9127, 9319, 9721, 11467, 12109, 13411, 13831, 15331, 15661, 17029, 17971, 17989, 19489, 21169, 23431, 24439, 24907, 25849, 26161, 31387, 33151, 34039, 34897, 36451, 37441, 37879

Offset: 1

Author

K. D. Bajpai, May 28 2014

Keywords

• nonn

Comments

Intersection of A062326 and A178251.

Examples

			19 is prime and appears in the sequence because [19^3-2 = 6857] and [19^2-2 = 359] are both primes.
37 is prime and appears in the sequence because [37^3-2 = 50651] and [37^2-2 = 1367] are both primes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001248, A030078, A062326, A178251.

Programs

Maple

with(numtheory):A242979:= proc() local p; p:=ithprime(n); if isprime(p^3-2) and isprime(p^2-2)then RETURN (p); fi; end: seq( A242979 (), n=1..5000);

Mathematica

c = 0; t=Prime[n]; Do[If[PrimeQ[t^3 - 2] && PrimeQ[t^2 - 2], c++; Print[c,"  ",t]], {n,1,3*10^6}];