

A307562


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


3



1, 2, 5, 6, 10, 11, 12, 16, 17, 25, 26, 32, 37, 45, 46, 51, 55, 61, 62, 72, 76, 90, 95, 100, 101, 102, 121, 122, 125, 137, 142, 146, 165, 172, 177, 181, 186, 187, 205, 215, 216, 220, 237, 241, 242, 247, 257, 270, 276, 277, 282, 290, 291, 292, 296, 297, 310, 311, 312, 331, 332, 335, 347, 355, 356, 380, 381, 390
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OFFSET

1,2


COMMENTS

There are 138 such numbers between 1 and 1000.
Prime pairs that differ by 6 are called "sexy" primes. Other prime pairs that differ by 6 are of the form 6n  1 and 6n + 5.
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



EXAMPLE

a(3) = 5, so 6(5) + 1 = 31 and 6(5) + 7 = 37 are both prime.


MATHEMATICA



PROG

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



