A258261 -id:A258261 - cp's OEIS frontend

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

David W. Wilson

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

			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.

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

Cf. A258261 (3p - 4).

[n: n in [0..1000] | IsPrime(n) and IsPrime(3*n+4)]; // Vincenzo Librandi, Nov 18 2010

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

isok(p) = isprime(p) && isprime(3*p+4); \\ Michel Marcus, Nov 09 2018

Name adjusted by Alonso del Arte, Nov 08 2018

A228353 Primes of the form 3p - 4 where p is prime.

Original entry on oeis.org

2, 5, 11, 17, 29, 47, 53, 83, 89, 107, 137, 173, 179, 197, 233, 263, 317, 389, 443, 449, 467, 569, 587, 593, 677, 683, 719, 809, 827, 839, 929, 947, 1097, 1163, 1187, 1223, 1259, 1289, 1367, 1433, 1493, 1523, 1559, 1619, 1637, 1667, 1709, 1847, 1889, 1973, 1979

Offset: 1

Irina Gerasimova, Aug 20 2013

Subsequence of A003627. - Michel Marcus, May 30 2015

Paolo P. Lava, Table of n, a(n) for n = 1..300

Cf. A228121, A258261, A003627.

Select[3*Prime[Range[200]]-4, PrimeQ] (* Zak Seidov, May 24 2015 *)

is(n)=n%3==2 && isprime(n\3+2) && isprime(n) \\ Charles R Greathouse IV, Mar 18 2014

a(n) = 3*A258261(n)-4. Zak Seidov, May 24 2015

a(n) >> n*log^2 n. - _Charles R Greathouse IV, Jun 04 2015

cp's OEIS Frontend

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

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