A239733 Primes p such that 4p+9 and 9p+4 are both prime.

7, 11, 23, 37, 41, 67, 71, 97, 113, 137, 163, 191, 197, 263, 307, 317, 401, 421, 491, 617, 653, 683, 727, 823, 881, 883, 907, 947, 953, 967, 1031, 1087, 1103, 1217, 1231, 1297, 1451, 1493, 1523, 1567, 1693, 1747, 1933, 1973, 2053, 2141, 2207, 2221, 2281, 2293

Offset

1,1

Comments

All numbers in this sequence are either 1, 3, or 7 mod 10.

Links

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

Example

7 is prime, 4*7+9 = 37 is prime, and 9*7+4 = 67 is prime. Thus, 7 is a member of this sequence.

Mathematica

Select[Prime[Range[400]], AllTrue[{4#+9, 9#+4}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 26 2014 *)

Prog

(Python)
import sympy
from sympy import isprime
{print(n) for n in range(5000) if isprime(4*n+9) and isprime(9*n+4) and isprime(n)}
(PARI) s=[]; forprime(p=2, 3000, if(isprime(4*p+9) && isprime(9*p+4), s=concat(s, p))); s \\ Colin Barker, Mar 26 2014

Crossrefs

Sequence in context: A255769 A175625 A082496 * A265768 A210001 A294074

Adjacent sequences: A239730 A239731 A239732 * A239734 A239735 A239736

Keyword

nonn,easy

Author

Derek Orr, Mar 25 2014

Status

approved