A243408 Primes p such that 10*p-1, 10*p-3, 10*p-7 and 10*p-9 are all prime.

2, 11, 83, 149, 347, 1301, 1607, 2531, 6299, 7727, 8273, 17117, 20183, 21737, 24371, 26669, 39227, 40277, 53951, 54917, 63347, 66359, 66467, 73637, 82217, 82373, 101537, 102251, 106397, 106871, 117203, 132971, 134033, 135221, 140237, 144701, 146141, 151433, 152597

Offset: 1

Author

Derek Orr, Jun 04 2014

Keywords

• nonn

Comments

This is a subsequence of A064975.

Examples

			2 is prime, 10*2-1 = 19 is prime, 10*2-3 = 17 is prime, 10*2-7 = 13 is prime, 10*2-9 = 11 is prime. Thus 2 is a member of this sequence.
		

Links

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

Crossrefs

Cf. A067267, A064975.

Programs

Mathematica

Select[ Range@ 153000,PrimeQ[#] && PrimeQ[10#-1] && PrimeQ[10#-3] && PrimeQ[10#-7] && PrimeQ[10#-9] &] (* Robert G. Wilson v, Jun 06 2014 *)
Select[Prime[Range[15000]],AllTrue[10#-{1,3,7,9},PrimeQ]&] (* Harvey P. Dale, Aug 18 2024 *)

PARI

for(n=1,10^5,if(ispseudoprime(10*prime(n)-1) && ispseudoprime(10*prime(n)-3) && ispseudoprime(10*prime(n)-7) && ispseudoprime(10*prime(n)-9),print1(prime(n),", ")))

Python

import sympy
from sympy import isprime
from sympy import prime
{print(prime(n),end=', ') for n in range(1,10**5) if isprime(10*prime(n)-1) and isprime(10*prime(n)-3) and isprime(10*prime(n)-7) and isprime(10*prime(n)-9)}