A164566 - OEIS

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A164566

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

4

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

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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