A307561 Numbers k such that both 6*k - 1 and 6*k + 5 are prime.

1, 2, 3, 4, 7, 8, 9, 14, 17, 18, 22, 28, 29, 32, 38, 39, 42, 43, 44, 52, 58, 59, 64, 74, 77, 84, 93, 94, 98, 99, 107, 108, 109, 113, 137, 143, 147, 157, 158, 162, 163, 169, 182, 183, 184, 197, 198, 203, 204, 213, 214, 217, 227, 228, 238, 239, 247, 248, 249, 259, 267, 268, 269, 312, 317, 318, 329, 333, 344

Offset

1,2

Comments

There are 146 terms below 10^3, 831 terms below 10^4, 5345 terms below 10^5, 37788 terms below 10^6 and 280140 terms below 10^7.

Prime pairs differing by 6 are called "sexy" primes. Other prime pairs with difference 6 are of the form 6n + 1 and 6n + 7.

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

Links

Amiram Eldar, 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(2) = 2, so 6(2) - 1 = 11 and 6(2) + 5 = 17 are both prime.

Mathematica

Select[Range[500], PrimeQ[6# - 1] && PrimeQ[6# + 5] &] (* Alonso del Arte, Apr 14 2019 *)

Prog

(PARI) is(k) = isprime(6*k-1) && isprime(6*k+5); \\ Jinyuan Wang, Apr 20 2019

Crossrefs

Primes differing from each other by 6 are A023201, A046117.

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

Intersection of A024898 and A059325.

Cf. also A307562, A307563.

Sequence in context: A349759 A050271 A322742 * A152037 A329295 A058075

Adjacent sequences: A307558 A307559 A307560 * A307562 A307563 A307564

Keyword

nonn

Author

Sally Myers Moite, Apr 14 2019

Status

approved