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Search: id:A105413
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| A105413 |
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Numbers p(n) such that both p(n)+2 and p(n+6)-2 are prime numbers, where p(n) is the n-th prime. |
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1
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| 3, 11, 107, 239, 311, 569, 1019, 1031, 1229, 1427, 1997, 2081, 2087, 2111, 2687, 3251, 4049, 4127, 4157, 4229, 4241, 4481, 5231, 5639, 6089, 7307, 7559, 8969, 9629, 10007, 10457, 13691, 13829, 13901, 14249, 14549, 14561, 16187, 16649, 17207
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture: There are an infinite number of primes p(n) such that p(n)-2 and p(n+k)-2 are both prime for all k > 1.
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EXAMPLE
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p(6)-2 = 11, p(6+5)-2 = 29, both prime, 1 is in the table.
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MATHEMATICA
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For[n = 1, n < 500, n++, If[PrimeQ[Prime[n] + 2], If[PrimeQ[Prime[n + 6] - 2], Print[Prime[n]]]]] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 07 2006
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PROGRAM
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(PARI) pnpk(n, m, k) = \ both are prime { local(x, l1, l2, v1, v2); for(x=1, n, v1 = prime(x)+ k; v2 = prime(x+m)+k; if(isprime(v1)&isprime(v2), \ print1(x", ") print1(v1", ") ) ) }
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CROSSREFS
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Sequence in context: A007616 A121045 A092245 this_sequence A136985 A131546 A068693
Adjacent sequences: A105410 A105411 A105412 this_sequence A105414 A105415 A105416
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), May 02 2005
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