A105411 Numbers p(n) such that both p(n)+2 and p(n+4)-2 are prime numbers, where p(n) is the n-th prime number (A000040(n)).

3, 17, 29, 59, 227, 269, 617, 1031, 1277, 1289, 1301, 1607, 1667, 1697, 2087, 2129, 2309, 2711, 2789, 3257, 3527, 3539, 3557, 3917, 4019, 4241, 4517, 4637, 4787, 5477, 5501, 5639, 6551, 7307, 8819, 8837, 8999, 9011, 10037, 10067, 10271, 10499, 12041

Offset

1,1

Comments

prime(7)=17, and both prime(7)+2=19 and prime(7+4)-2=29 are prime, so 17 is in the sequence.

Essentially the same as A089629. - R. J. Mathar, Aug 28 2008

Links

Table of n, a(n) for n=1..43.

Mathematica

For[n = 1, n < 500, n++, If[PrimeQ[Prime[n] + 2], If[PrimeQ[Prime[n + 4] - 2], Print[Prime[n]]]]] (* Stefan Steinerberger, Feb 07 2006 *)
Select[Partition[Prime[Range[1500]], 5, 1], AllTrue[{#[[1]]+2, #[[5]]-2}, PrimeQ]&][[All, 1]] (* Harvey P. Dale, Oct 28 2022 *)

Prog

(PARI) pnpk(n, m=4, 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+4)-2)]; // Vincenzo Librandi, Sep 14 2015

Crossrefs

Sequence in context: A173587 A022887 A063715 * A107158 A188620 A152529

Adjacent sequences: A105408 A105409 A105410 * A105412 A105413 A105414

Keyword

nonn

Author

Cino Hilliard, May 02 2005

Status

approved