A023209 Primes p such that 3p + 4 is also prime.

3, 5, 11, 13, 19, 23, 31, 41, 53, 59, 73, 79, 89, 101, 103, 109, 131, 139, 151, 173, 179, 181, 191, 199, 223, 229, 241, 251, 269, 283, 293, 311, 331, 349, 353, 373, 383, 389, 409, 431, 433, 439, 509, 521, 541, 563, 593, 599, 619, 643, 661, 683, 709, 719, 733, 739, 761

Offset

1,1

Comments

In order for 3p + 4 to also be in the sequence, it is a necessary but not sufficient condition that p is not congruent to 7 modulo 10. - Alonso del Arte, Nov 08 2018

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

3 and 3 * 3 + 4 = 13 are both prime, so 3 is in the sequence.
5 and 3 * 5 + 4 = 19 are both prime, so 5 is in the sequence.
7 is prime but 3 * 7 + 4 = 25 = 5^2, which is not prime, so 7 is not in the sequence.

Mathematica

Select[Prime[Range[500]], PrimeQ[3# + 4] &] (* Harvey P. Dale, Mar 09 2014 *)

Prog

(Magma) [n: n in [0..1000] | IsPrime(n) and IsPrime(3*n+4)]; // Vincenzo Librandi, Nov 18 2010
(PARI) isok(p) = isprime(p) && isprime(3*p+4); \\ Michel Marcus, Nov 09 2018

Crossrefs

Cf. A258261 (3p - 4).

Sequence in context: A136208 A045405 A059311 * A020609 A151917 A059639

Adjacent sequences: A023206 A023207 A023208 * A023210 A023211 A023212

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Name adjusted by Alonso del Arte, Nov 08 2018

Status

approved