A046117 Primes p such that p-6 is also prime. (Upper of a pair of sexy primes.)

11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 89, 103, 107, 109, 113, 137, 157, 163, 173, 179, 197, 199, 229, 233, 239, 257, 263, 269, 277, 283, 313, 317, 337, 353, 359, 373, 379, 389, 439, 449, 463, 467, 509, 547, 563, 569, 577, 593, 599, 607, 613

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- N. J. A. Sloane, Mar 07 2021].

Formula

a(n) = A087695(n) + 3.

a(n) = A023201(n) + 6. - M. F. Hasler, Jan 02 2020

Mathematica

q=6; a={}; Do[p1=Prime[n]; p2=p1+q; If[PrimeQ[p2], AppendTo[a, p2]], {n, 7^2}]; a "and/or" Select[Prime[Range[3, 7^2]], PrimeQ[ # ]&&PrimeQ[ #-6]&] (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)
Select[Prime[Range[4, 200]], PrimeQ[#-6]&] (* Harvey P. Dale, Mar 31 2018 *)

Prog

(PARI) forprime(p=2, 1e4, if(isprime(p-6), print1(p", "))) \\ Charles R Greathouse IV, Jul 15 2011
(Magma) [p:p in PrimesInInterval(7, 650)| IsPrime(p-6)]; // Marius A. Burtea, Jan 03 2020

Crossrefs

Cf. A023201, A098428, A087695.

Sequence in context: A052293 A038842 A293660 * A240900 A091923 A046501

Adjacent sequences: A046114 A046115 A046116 * A046118 A046119 A046120

Keyword

nonn,changed

Author

Eric W. Weisstein

Extensions

Name edited by M. F. Hasler, Jan 02 2020

Status

approved