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

KEYWORD

nonn

AUTHOR

Sally Myers Moite, Apr 14 2019

STATUS

approved