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 A105412 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. 0
 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; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Table of n, a(n) for n=1..42. EXAMPLE prime(13)=41, and both prime(13)+2=43 and prime(13+5)-2=59 are prime, so 41 is in the sequence. MATHEMATICA For[n = 1, n < 500, n++, If[PrimeQ[Prime[n] + 2], If[PrimeQ[Prime[n + 5] - 2], Print[Prime[n]]]]] (* Stefan Steinerberger, Feb 07 2006 *) PROG (PARI) pnpk(n, m=5, k=2) = { local(x, v1, v2); for(x=1, n, v1 = prime(x)+ k; v2 = prime(x+m)-k; if(isprime(v1)&isprime(v2), print1(prime(x), ", ") ) ) ; } \\ corrected by Michel Marcus, Sep 14 2015 (Magma) [NthPrime(n): n in [1..1500] | IsPrime(NthPrime(n)+2) and IsPrime(NthPrime(n+5)-2)]; // Vincenzo Librandi, Sep 14 2015 CROSSREFS Sequence in context: A128347 A349336 A056905 * A271017 A270674 A271001 Adjacent sequences: A105409 A105410 A105411 * A105413 A105414 A105415 KEYWORD nonn AUTHOR Cino Hilliard, May 02 2005 STATUS approved

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Last modified July 22 00:58 EDT 2024. Contains 374478 sequences. (Running on oeis4.)