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A307563
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Numbers k such that both 6k - 1 and 6k + 7 are prime.
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3
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(4) = 5, so 6(5) - 1 = 29 and 6(5) + 7 = 37 are both prime.
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MAPLE
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select(t -> isprime(6*t-1) and isprime(6*t+7), [$1..500]); # Robert Israel, May 27 2019
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PROG
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(PARI) isok(n) = isprime(6*n-1) && isprime(6*n+7); \\ Michel Marcus, Apr 16 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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