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

Offset: 1

Author

David W. Wilson

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A045392, A105772.

Programs

Magma

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

Mathematica

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

PARI

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