A352170 Primes p such that p+4, 3*p+4 and 3*p+8 are also prime.

3, 13, 103, 223, 823, 2953, 7873, 11113, 11863, 13033, 13963, 16063, 22153, 23743, 24763, 27733, 30133, 31513, 34213, 35593, 39883, 41893, 43063, 50383, 51043, 54493, 62983, 65323, 66343, 68473, 71593, 72643, 87793, 88423, 98893, 101203, 106363, 110563, 127873, 134593, 136603, 158563, 164623, 165703

Offset

1,1

Comments

Members p of A023200 such that 3*p+4 is also in A023200.

Except for 3, all terms == 13 (mod 30).

Links

Martin Ehrenstein, Table of n, a(n) for n = 1..10000

Example

a(4) = 223 is a term because 223, 223+4 = 227, 3*223+4 = 673 and 3*223+8 = 677 are all prime.

Maple

select(p -> isprime(p) and isprime(p+4) and isprime(3*p+4) and isprime(3*p+8), [3, seq(i, i=13..10^6, 30)]);

Mathematica

Select[Range[200000], AllTrue[{#, # + 4, 3*# + 4, 3*# + 8}, PrimeQ] &] (* Amiram Eldar, Mar 07 2022 *)

Prog

(Python)
from sympy import sieve, isprime
for p in sieve.primerange(0, 10**6):
    if(all(isprime(q) for q in [p+4, 3*p+4, 3*p+8])):
        print (p, end=", ") # Martin Ehrenstein, Mar 09 2022

Crossrefs

Intersection of A023200, A023209 and A023210.

Sequence in context: A323687 A338697 A168417 * A240167 A127004 A068168

Adjacent sequences: A352167 A352168 A352169 * A352171 A352172 A352173

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Mar 07 2022

Status

approved