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A307563
Numbers k such that both 6k - 1 and 6k + 7 are prime.
3
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.
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
KEYWORD
nonn
AUTHOR
Sally Myers Moite, Apr 14 2019
STATUS
approved