A307563 Numbers k such that both 6k - 1 and 6k + 7 are prime.

1, 2, 4, 5, 9, 10, 12, 15, 17, 22, 25, 29, 32, 39, 44, 45, 60, 65, 67, 72, 75, 80, 82, 94, 95, 99, 100, 109, 114, 117, 120, 124, 127, 137, 152, 155, 164, 169, 172, 177, 185, 194, 199, 204, 205, 214, 215, 220, 229, 240, 242, 247, 254, 260, 262, 267, 269, 270, 289, 304, 312, 330, 334, 347, 355, 359, 369, 374, 379, 389

Offset

1,2

Comments

There are 140 such numbers between 1 and 1000.

These numbers correspond to all the prime pairs which differ by 8 except 3 and 11.

Numbers in this sequence are those which are not 6cd - c - d - 1, 6cd + c - d, 6cd - c + d or 6cd + c + d - 1, that is, they are not (6c - 1)d - c - 1, (6c - 1)d + c, (6c + 1)d - c or (6c + 1)d + c - 1.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Sally M. Moite, “Primeless” Sieves for Primes and for Prime Pairs Which Differ by 2m, vixra:1903.0353 (2019).

Example

a(4) = 5, so 6(5) - 1 = 29 and 6(5) + 7 = 37 are both prime.

Maple

select(t -> isprime(6*t-1) and isprime(6*t+7), [$1..500]); # Robert Israel, May 27 2019

Prog

(PARI) isok(n) = isprime(6*n-1) && isprime(6*n+7); \\ Michel Marcus, Apr 16 2019

Crossrefs

The primes are A023202, A092402, A031926.

Similar sequences for twin primes are A002822, A067611, for "cousin" primes A056956, A186243.

Intersection of A024898 and A153218.

Cf. also A307561, A307562.

Sequence in context: A342750 A047613 A036795 * A289175 A274693 A024618

Adjacent sequences: A307560 A307561 A307562 * A307564 A307565 A307566

Keyword

nonn

Author

Sally Myers Moite, Apr 14 2019

Status

approved