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A023330 Primes that remain prime through 5 iterations of function f(x) = 2x + 1.

%I A023330 #44 Feb 09 2024 10:09:13
%S A023330 89,63419,127139,405269,810809,1069199,1122659,1178609,1333889,
%T A023330 1598699,1806089,1958249,2164229,2245319,2329469,2606069,2848949,
%U A023330 3241289,3339989,3784199,3962039,4088879,4328459,4444829,4658939,4664249,4894889,4897709,5132999
%N A023330 Primes that remain prime through 5 iterations of function f(x) = 2x + 1.
%C A023330 Primes p such that 2*p+1, 4*p+3, 8*p+7, 16*p+15 and 32*p+31 are also primes. - _Vincenzo Librandi_, Aug 04 2010
%H A023330 Donovan Johnson, <a href="/A023330/b023330.txt">Table of n, a(n) for n = 1..1000</a>
%F A023330  a(n) == 29 (mod 30). - _Zak Seidov_, Jan 31 2013
%t A023330 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 *)
%o A023330 (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
%o A023330 (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
%o A023330 (Python)
%o A023330 from sympy import prime, isprime
%o A023330 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
%Y A023330 Cf. A005384, A005385, A007700, A023272, A023302, A057331, A005602.
%K A023330 nonn
%O A023330 1,1
%A A023330 _David W. Wilson_