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

2, 53639, 53849, 61409, 66749, 143609, 167729, 186149, 206369, 268049, 296099, 340919, 422069, 446609, 539009, 594449, 607319, 658349, 671249, 725009, 775949, 812849, 819509, 926669, 1008209, 1092089, 1132949, 1271849

Offset

1,1

Links

Table of n, a(n) for n=1..28.

Chris Caldwell's Prime Glossary, Cunningham chains.

Formula

{(p-1)/2, p, 2p+1, 4p+3, 8p+7, 16p+15, 32p+31} = {nonprime, prime, prime, prime, prime, prime, composite}

Example

2 is here because (2-1)/2=1/2 and 32*2+31=95 are not primes, while 2,5,11,23,47 gives a first-kind-Cu5-chain of 5 primes which cannot be continued.
53639 is here because through <2p+1>, 53639 -> 107279 -> 214559 -> 429119 -> 858239 and the chain ends here (with this operator).

Mathematica

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 *)

Crossrefs

Cf. A023272, A023302, A023330, A005384, A005385, A059452-A059455, A007700, A059759, A059760, A059761, A059762, A059763, A059764, A059765, A038397, A104349, A091314, A069362, A016093, A014937, A057326.

Sequence in context: A094213 A321382 A153924 * A285694 A306907 A052427

Adjacent sequences: A059761 A059762 A059763 * A059765 A059766 A059767

Keyword

nonn

Author

Labos Elemer, Feb 20 2001

Extensions

Definition corrected by Alexandre Wajnberg, Aug 31 2005

Entry revised by N. J. A. Sloane, Apr 01 2006

Status

approved