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

1,1

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.

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

Prog

(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

Crossrefs

Subsequence of A007522.

Sequence in context: A329010 A309855 A364845 * A232446 A362491 A202558

Adjacent sequences: A339579 A339580 A339581 * A339583 A339584 A339585

Keyword

nonn

Author

N. J. A. Sloane, Dec 24 2020

Extensions

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

Status

approved