

A164566


Primes p such that 7*p6 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, 7*56=29 and 7*5+6=41 are prime, so 5 enters the sequence.
For p=11, 7*116=71 and 7*11+6=83 are prime, so 11 enters the sequence.


MATHEMATICA

lst={}; Do[p=Prime[n]; If[PrimeQ[7*p6]&&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*p6) and IsPrime(7*p+6)]; // Vincenzo Librandi, Apr 09 2013


CROSSREFS

Cf. A106015, A125272, A127430, A046133, A087681, A136052, A023225.
Sequence in context: A191032 A003147 A106068 * 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



