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Search: id:A105412
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| A105412 |
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Numbers p(n) such that both p(n)+2 and p(n+5)-2 are prime numbers, where p(n) is the n-th prime number. |
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| 5, 41, 179, 197, 281, 599, 641, 809, 827, 857, 1061, 1451, 2237, 2549, 3119, 3329, 3359, 3821, 4001, 4091, 4217, 5417, 5441, 5849, 6269, 6659, 6761, 6791, 7457, 7949, 8387, 8597, 9239, 9419, 9431, 9677, 10301, 10427, 10859, 10889, 11117, 11717
(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 is an infinity 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(14) -2 = 41, p(14+4)-2 = 59, both prime.
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MATHEMATICA
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For[n = 1, n < 500, n++, If[PrimeQ[Prime[n] + 2], If[PrimeQ[Prime[n + 5] - 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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Adjacent sequences: A105409 A105410 A105411 this_sequence A105413 A105414 A105415
Sequence in context: A128347 A056905 A088547 this_sequence A096946 A027954 A083300
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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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