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

1,1

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

Cf. A045392, A105772.

Sequence in context: A133914 A169913 A260239 * A106086 A072828 A290114

Adjacent sequences: A023220 A023221 A023222 * A023224 A023225 A023226

Keyword

nonn

Author

David W. Wilson

Status

approved