cp's OEIS Frontend

A059764 Initial (unsafe) primes of Cunningham chains of first type with length exactly 5. Primes in A059453 that survive as primes just four "2p+1 iterations", forming chains of exactly 5 terms.

%I A059764 #22 Jul 15 2024 10:23:29
%S A059764 2,53639,53849,61409,66749,143609,167729,186149,206369,268049,296099,
%T A059764 340919,422069,446609,539009,594449,607319,658349,671249,725009,
%U A059764 775949,812849,819509,926669,1008209,1092089,1132949,1271849
%N A059764 Initial (unsafe) primes of Cunningham chains of first type with length exactly 5. Primes in A059453 that survive as primes just four "2p+1 iterations", forming chains of exactly 5 terms.
%C A059764 Primes p such that {(p-1)/2, p, 2p+1, 4p+3, 8p+7, 16p+15, 32p+31} = {nonprime, prime, prime, prime, prime, prime, composite}.
%H A059764 Amiram Eldar, <a href="/A059764/b059764.txt">Table of n, a(n) for n = 1..10000</a>
%H A059764 Chris Caldwell's Prime Glossary, <a href="https://t5k.org/glossary/page.php?sort=CunninghamChain">Cunningham chains</a>.
%e A059764 2 is here because (2-1)/2 = 1/2 and 32*2+31 = 95 are not primes, while 2, 5, 11, 23, and 47 give a first-kind Cunningham chain of 5 primes which cannot be continued.
%e A059764 53639 is here because through <2p+1>, 53639 -> 107279 -> 214559 -> 429119 -> 858239 and the chain ends here (with this operator).
%t A059764 l5Q[n_]:=Module[{a=PrimeQ[(n-1)/2],b=PrimeQ[ NestList[2#+1&,n,5]]}, Join[{a},b]=={False,True,True,True,True,True,False}]; Select[Range[ 1300000],l5Q] (* _Harvey P. Dale_, Oct 14 2012 *)
%Y A059764 Cf. A023272, A023302, A023330, A005384, A005385, A059452-A059455, A007700, A059759, A059760, A059761, A059762, A059763, A059764, A059765, A038397, A104349, A091314, A069362, A016093, A014937, A057326.
%K A059764 nonn
%O A059764 1,1
%A A059764 _Labos Elemer_, Feb 20 2001
%E A059764 Definition corrected by _Alexandre Wajnberg_, Aug 31 2005
%E A059764 Entry revised by _N. J. A. Sloane_, Apr 01 2006