A105412 Primes p = prime(k) such that both p+2 and prime(k+5)-2 are prime numbers.

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

Offset

1,1

Comments

Conjecture: There are infinitely many primes p(k) such that p(k)+2 and p(k+m)-2 are both primes for all m > 1.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

prime(13) = 41, and both prime(13)+2 = 43 and prime(13+5)-2 = 59 are primes, 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
(PARI) lista(pmax) = {my(k = 1, p = primes(6)); forprime(p1 = p[#p], pmax, k++; p[#p] = p1; if(p[2]- p[1] == 2 && p[6] - p[5] == 2, print1(p[1], ", ")); for(i = 1, #p-1, p[i] = p[i+1])); } \\ Amiram Eldar, Oct 04 2024
(Magma) [NthPrime(n): n in [1..1500] | IsPrime(NthPrime(n)+2) and IsPrime(NthPrime(n+5)-2)]; // Vincenzo Librandi, Sep 14 2015

Crossrefs

Cf. A105409, A105410, A105411, A105413, A105414.

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