A240126 Primes p such that p - 2 and p^3 - 2 are also prime.

19, 31, 109, 151, 241, 619, 859, 1489, 1951, 2131, 2791, 2971, 3559, 4129, 4651, 4789, 4801, 5659, 6661, 6781, 7591, 8221, 8629, 8821, 8971, 9241, 9721, 9931, 10891, 11971, 12109, 12541, 13831, 14011, 15271, 15289, 15331, 16831, 17029, 17419, 17839, 17989, 18121, 18541, 20149, 20899, 21019

Offset

1,1

Comments

All the terms in the sequence are congruent to 1 mod 3.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..3085

Example

19 is in the sequence because 19 is a prime: 19 - 2 = 17 and 19^3 - 2 = 6857 are also prime.
151 is in the sequence because 151 is a prime: 151 - 2 = 149 and 151^3 - 2 = 3442949 are also prime.

Maple

KD := proc() local a, b, d; a:=ithprime(n); b:=a-2; d:=a^3-2;  if isprime(b)and isprime(d) then RETURN (a); fi; end: seq(KD(), n=1..10000);

Mathematica

Select[Prime[Range[2000]], PrimeQ[# - 2] && PrimeQ[#^3 - 2] &]

Prog

(PARI) s=[]; forprime(p=2, 22000, if(isprime(p-2) && isprime(p^3-2), s=concat(s, p))); s \\ Colin Barker, Apr 02 2014

Crossrefs

Intersection of A006512 and A178251.

Cf. A048637, A140454, A175234, A236687, A236688, A240110.

Sequence in context: A107168 A243450 A237418 * A125602 A139847 A087764

Adjacent sequences: A240123 A240124 A240125 * A240127 A240128 A240129

Keyword

nonn

Author

K. D. Bajpai, Apr 01 2014

Status

approved