A109998 - OEIS

%I #19 Apr 03 2023 10:36:10

%S 17,43,67,71,101,103,109,127,137,149,151,163,181,197,223,241,257,269,

%T 283,311,317,349,353,373,389,401,409,433,449,461,463,487,521,523,557,

%U 569,571,599,617,631,643,647,677,701,709,739,751,769,773,787,797,821

%N Non-Cunningham primes: primes isolated from any Cunningham chain under any iteration of 2p+-1 or (p+-1)/2.

%C The condition that neither 2p - 1 nor 2p + 1 be prime is equivalent to ((p-1) mod 3 = 0) or ((p+1) mod 3 = 0). For example, the prime p = 2^607 - 1 is not in this sequence because p + 1 mod 3 = 2. - _Washington Bomfim_, Oct 30 2009

%H Chris Caldwell's Prime Glossary, <a href="https://t5k.org/glossary/page.php?sort=CunninghamChain">Cunningham chains</a>.

%H Douglas S. Stones, <a href="http://arxiv.org/abs/0908.2166">On prime chains</a>, arXiv:0908.2166 [math.NT] [From _Washington Bomfim_, Oct 30 2009, edited by _R. J. Mathar_, Mar 01 2010]

%e a(1) = 17 is here because 17 * 2 + 1 = 35, 17 * 2 - 1 = 33; (17+1)/2 = 9, (17-1)/2 = 8: four composite numbers.

%t nonCunninghamPrimes = {}; Do[p = Prime[n]; If[!PrimeQ[2p - 1] && !PrimeQ[2p + 1] && !PrimeQ[(p - 1)/2] && !PrimeQ[(p + 1)/2], AppendTo[nonCunninghamPrimes, p]], {n, 6!}]; nonCunninghamPrimes (* _Vladimir Joseph Stephan Orlovsky_, Mar 22 2009 *)

%Y Cf. A005385, A005383, A060254, A005384, A005382, A068497, A059455, A059762, A057326, A023272, A023302, A059764, A057328, A023330, A005602, A064812, A005603.

%K easy,nonn

%O 1,1

%A _Alexandre Wajnberg_, Sep 01 2005

%E Corrected and extended by _Ray Chandler_, Sep 02 2005

%E Replaced link to cached arXiv URL with link to the abstract - _R. J. Mathar_, Mar 01 2010