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

1,1

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A048637 A128551 A154942 * A228502 A215663 A381200

Adjacent sequences: A240107 A240108 A240109 * A240111 A240112 A240113

Keyword

nonn

Author

K. D. Bajpai, Apr 01 2014

Status

approved