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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 (list; graph; refs; listen; history; text; internal format)
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
Select[Range[400], AllTrue[6 # + {1, 7}, PrimeQ] &] (* Michael De Vlieger, Apr 15 2019 *)
PROG
(PARI) isok(n) = isprime(6*n+1) && isprime(6*n+7); \\ Michel Marcus, Apr 16 2019
CROSSREFS
For the primes see A023201, A046117.
Similar sequences for twin primes are A002822, A067611, for "cousin" primes A056956, A186243.
Intersection of A024899 and A153218.
Cf. also A307561, A307563.
Sequence in context: A184418 A112967 A244731 * A109150 A004202 A013647
KEYWORD
nonn
AUTHOR
Sally Myers Moite, Apr 14 2019
STATUS
approved

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Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)