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A023330 Numbers n such that n remains prime through 5 iterations of function f(x) = 2x + 1. 34
89, 63419, 127139, 405269, 810809, 1069199, 1122659, 1178609, 1333889, 1598699, 1806089, 1958249, 2164229, 2245319, 2329469, 2606069, 2848949, 3241289, 3339989, 3784199, 3962039, 4088879, 4328459, 4444829, 4658939, 4664249, 4894889, 4897709, 5132999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

n, 2*n+1, 4*n+3, 8*n+7, 16*n+15 and 32*n+31 are primes. - Vincenzo Librandi, Aug 04 2010

All terms == 29 mod 30. That should be used in the codes. - Zak Seidov, Jan 31 2013

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..1000

MAPLE

List023330:= proc(q) local a, b, n;

for n from 1 to q do

  if ithprime(n) mod 30=29 then a:=-1; b:=2*ithprime(n)+1;

   while isprime(b) do a:=a+1; b:=2*b+1; od; if a=4 then lprint(ithprime(n), a);

fi; fi; od; end:

List023330 (10^10); # Paolo P. Lava, Apr 05 2013

MATHEMATICA

Select[Prime[Range[10^5]], PrimeQ[a1=2*#+1] && PrimeQ[a2=2*a1+1] && PrimeQ[a3=2*a2+1] && PrimeQ[a4=2*a3+1] && PrimeQ[a5=2*a4+1] &] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)

PROG

(MAGMA) [n: n in [1..5000000] | forall{2^i*n+2^i-1: i in [0..5] | IsPrime(2^i*n+2^i-1)}]; // Vincenzo Librandi, Aug 04 2010

(PARI) is(n)=isprime(n) && isprime(2*n+1) && isprime(4*n+3) && isprime(8*n+7) && isprime(16*n+15) && isprime(32*n+31) \\ Charles R Greathouse IV, Jul 01 2013

(Python)

from sympy import prime, isprime

A023330_list = [p for p in (prime(n) for n in range(1, 10**5)) if all([isprime(2**m*(p+1)-1) for m in range(1, 6)])] # Chai Wah Wu, Sep 09 2014

CROSSREFS

Cf. A005384, A005385, A007700, A023272, A023302, A057331, A005602.

Sequence in context: A174758 A181681 A167398 * A059766 A033513 A128872

Adjacent sequences:  A023327 A023328 A023329 * A023331 A023332 A023333

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified November 20 20:56 EST 2019. Contains 329347 sequences. (Running on oeis4.)