A240110 Primes p such that p+2 and p^3+2 are also prime.

3, 5, 29, 71, 311, 419, 431, 1031, 1091, 1151, 1451, 1931, 2339, 3371, 3461, 4001, 4421, 4799, 5651, 6269, 6551, 6569, 6761, 6779, 6869, 7559, 7589, 8219, 9011, 9281, 10301, 11069, 11489, 11549, 12161, 12239, 12251, 12539, 14081, 15641, 17189, 18059, 18119, 18521

Offset: 1

Author

K. D. Bajpai, Apr 01 2014

Keywords

• nonn

Comments

All the terms in the sequence, except a(1), are congruent to 2 mod 3.

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..3166

Crossrefs

Cf. A000040, A048637, A140454, A175234, A236687, A236688.

Programs

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[2200]],AllTrue[{#+2,#^3+2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 14 2017 *)

PARI

s=[]; forprime(p=2, 20000, if(isprime(p+2) && isprime(p^3+2), s=concat(s, p))); s \\ Colin Barker, Apr 01 2014