A339582 Primes p = 8*r-1 such that all the prime factors of r are 7 mod 12.

7, 151, 631, 823, 1063, 1303, 1783, 2647, 2887, 3511, 4423, 4567, 4951, 5527, 6007, 6871, 7351, 7687, 7927, 8311, 9127, 10663, 11383, 11863, 12007, 12343, 12487, 13591, 14071, 15031, 15607, 15991, 16087, 17047, 17191, 17431, 17623, 17911, 19207, 20023, 20407

Offset: 1

Author

N. J. A. Sloane, Dec 24 2020

Keywords

• nonn

Comments

Hugh Williams asks if this sequence is infinite.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• R. K. Guy, editor, Western Number Theory Problems, 1985-12-21 & 23, Typescript, Jul 13 1986, Dept. of Math. and Stat., Univ. Calgary, 11 pages. Annotated scan of pages 1, 3, 7, 9, with permission. See Problem 85:16.

Crossrefs

Subsequence of A007522.

Programs

Maple

filter:= n ->
  isprime(n) and numtheory:-factorset((n+1)/8) mod 12 subset {7}:
select(filter, [seq(i,i=7..10^5,8)]); # Robert Israel, Dec 24 2020

PARI

isok(p) = if (isprime(p) && (Mod(p, 8)== -1), my(r=(p+1)/8, f=factor(r)[,1]); #select(x->(Mod(x, 12) == 7), f) == #f); \\ Michel Marcus, Dec 24 2020

Extensions

More terms from Michel Marcus, Dec 24 2020, who also added the initial term 7.