A164566 Primes p such that 7*p-6 and 7*p+6 are also prime numbers.

5, 11, 19, 31, 41, 61, 71, 109, 151, 211, 229, 269, 379, 419, 431, 439, 479, 619, 641, 709, 739, 809, 839, 971, 1009, 1069, 1229, 1259, 1319, 1361, 1439, 1451, 1499, 1531, 1579, 1669, 1801, 1879, 1889, 2011, 2111, 2239, 2269, 2381, 2411, 2551, 2579, 2591

Offset

1,1

Comments

Primes of the form A087681(k)/7, any index k.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

A136052 INTERSECT A023225. [R. J. Mathar, Aug 20 2009]

Example

For p=5, both 7*5-6=29 and 7*5+6=41 are prime,
for p=11, both 7*11-6=71 and 7*11+6=83 are prime.

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[7*p-6]&&PrimeQ[7*p+6], AppendTo[lst, p]], {n, 6!}]; lst
Select[Prime[Range[700]], And @@ PrimeQ/@{7 # + 6, 7 # - 6}&] (* Vincenzo Librandi, Apr 09 2013 *)

Prog

(Magma) [p: p in PrimesUpTo(3000) | IsPrime(7*p-6) and IsPrime(7*p+6)]; // Vincenzo Librandi, Apr 09 2013
(PARI) is(n)=isprime(n) && isprime(7*n-6) && isprime(7*n+6) \\ Charles R Greathouse IV, Mar 28 2017

Crossrefs

Cf. A106015, A125272, A127430, A046133, A087681, A136052, A023225.

Sequence in context: A003147 A106068 A304875 * A075322 A079850 A065995

Adjacent sequences: A164563 A164564 A164565 * A164567 A164568 A164569

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Extensions

Examples rephrased by R. J. Mathar, Aug 20 2009

Status

approved