A023276 Primes that remain prime through 3 iterations of function f(x) = 2x + 9.

5, 11, 31, 71, 281, 521, 911, 1181, 2371, 2521, 3391, 3701, 4211, 4931, 5051, 7211, 7411, 8221, 8431, 8461, 8501, 8641, 8951, 9601, 9871, 10301, 11981, 12421, 13121, 13921, 14591, 16381, 16451, 16901, 16931, 17791, 17881, 19391, 19751, 21991, 23021

Offset

1,1

Comments

Primes p such that 2*p+9, 4*p+27 and 8*p+63 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

John Cerkan, Table of n, a(n) for n = 1..10000

Formula

a(n) == 1 (mod 10) for n > 1. - John Cerkan, Sep 16 2016

Maple

A023276:=n->`if`(isprime(n) and isprime(2*n+9) and isprime(4*n+27) and isprime(8*n+63), n, NULL): seq(A023276(n), n=1..10^5); # Wesley Ivan Hurt, Feb 11 2017

Mathematica

Select[Prime@ Range@ 2600, Times @@ Boole@ PrimeQ@ Rest@ NestList[2 # + 9 &, #, 3] > 0 &] (* Michael De Vlieger, Sep 19 2016 *)
Select[Prime[Range[3000]], AllTrue[Rest[NestList[2#+9&, #, 3]], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 01 2017 *)

Prog

(Magma) [n: n in [1..100000] | IsPrime(n) and IsPrime(2*n+9) and IsPrime(4*n+27) and IsPrime(8*n+63)] // Vincenzo Librandi, Aug 04 2010
(PARI) is(n)=isprime(n) && isprime(2*n+9) && isprime(4*n+27) && isprime(8*n+63) \\ Charles R Greathouse IV, Sep 20 2016

Crossrefs

Subsequence of A023207, A023245, and of A155722.

Sequence in context: A106088 A246010 A077446 * A074648 A236428 A106908

Adjacent sequences: A023273 A023274 A023275 * A023277 A023278 A023279

Keyword

nonn

Author

David W. Wilson

Status

approved