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A307561 Numbers k such that both 6*k - 1 and 6*k + 5 are prime. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A321699 A050271 A322742 * A152037 A329295 A058075

Adjacent sequences:  A307558 A307559 A307560 * A307562 A307563 A307564

KEYWORD

nonn

AUTHOR

Sally Myers Moite, Apr 14 2019

STATUS

approved

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Last modified May 18 07:26 EDT 2021. Contains 343995 sequences. (Running on oeis4.)