

A109998


NonCunningham primes: primes isolated from any Cunningham chain under any iteration of 2p+1 or (p+1)/2.


5



17, 43, 67, 71, 101, 103, 109, 127, 137, 149, 151, 163, 181, 197, 223, 241, 257, 269, 283, 311, 317, 349, 353, 373, 389, 401, 409, 433, 449, 461, 463, 487, 521, 523, 557, 569, 571, 599, 617, 631, 643, 647, 677, 701, 709, 739, 751, 769, 773, 787, 797, 821
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OFFSET

1,1


COMMENTS

The condition that neither 2p  1 nor 2p + 1 be prime is equivalent to ((p1) 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


LINKS



EXAMPLE

a(1) = 17 is here because 17 * 2 + 1 = 35, 17 * 2  1 = 33; (17+1)/2 = 9, (171)/2 = 8: four composite numbers.


MATHEMATICA

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 *)


CROSSREFS

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


KEYWORD

easy,nonn


AUTHOR



EXTENSIONS

Replaced link to cached arXiv URL with link to the abstract  R. J. Mathar, Mar 01 2010


STATUS

approved



