A023223 - OEIS

A023223

Primes p such that 7*p + 2 is also prime.

3, 5, 11, 23, 47, 53, 71, 101, 107, 131, 167, 173, 197, 251, 257, 293, 311, 317, 353, 383, 431, 461, 467, 563, 587, 593, 683, 701, 773, 797, 821, 827, 863, 887, 911, 953, 977, 983, 1031, 1091, 1097, 1103, 1151, 1181, 1187, 1193, 1217, 1223, 1277, 1301, 1307, 1373

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OFFSET

1,1

COMMENTS

Subsequence of A105772. Except for the first term all others are congruent to 5 (mod 6) because 7*(6n+1)+2 is divisible by 3. - John Cerkan, Jul 08 2016

LINKS

John Cerkan, Table of n, a(n) for n = 1..10000

EXAMPLE

3 is in the sequence because 7 * 3 + 2 = 23, which is prime.

5 is in the sequence because 7 * 5 + 2 = 37, which is prime.

7 is not in the sequence because 7 * 7 + 2 = 51 = 3 * 17.

MATHEMATICA

Select[Prime[Range[250]], PrimeQ[7# + 2] &] (* Alonso del Arte, Apr 08 2015 *)

PROG

(Magma) [n: n in [0..100000] | IsPrime(n) and IsPrime(7*n+2)]; // Vincenzo Librandi, Nov 19 2010

(PARI) lista(nn) = forprime(p=2, nn, if(isprime(7*p+2), print1(p, ", "))); \\ Altug Alkan, Jul 08 2016

CROSSREFS