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A059762 Initial primes of Cunningham chains of first type with length exactly 3. Primes in A059453 which survive as primes just two "2p+1 iterations", forming chains of exactly 3 terms. 17
41, 1031, 1451, 1481, 1511, 1811, 1889, 1901, 1931, 3449, 3491, 3821, 3911, 5081, 5441, 5849, 6101, 6131, 7151, 7349, 7901, 8969, 9221, 10691, 10709, 11171, 11471, 11801, 12101, 12821, 12959, 13229, 14009, 14249, 14321, 14669, 14741, 15161 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..37.

Chris Caldwell's Prime Glossary, Cunningham chains.

Warut Roonguthai, Yves Gallot's Proth.exe and Cunningham Chains.

Eric Weisstein's World of Mathematics, Cunningham Chain.

FORMULA

{(p-1)/2, p, 2p+1, 4p+3, 8p+7} = {composite, prime, prime, prime, composite}

EXAMPLE

41 is here because 20 and 325 are composites,41,83,167 are primes.

MATHEMATICA

ipccQ[n_]:=Module[{c=(n-1)/2}, PrimeQ[NestList[2#+1&, c, 4]]=={False, True, True, True, False}]; Select[Prime[Range[2000]], ipccQ] (* Harvey P. Dale, Nov 10 2014 *)

CROSSREFS

Cf. A023272, A023302, A023330, A005384, A005385, A059452-A059455, A007700.

Sequence in context: A038397 A104349 A091314 * A069362 A016093 A130639

Adjacent sequences:  A059759 A059760 A059761 * A059763 A059764 A059765

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 20 2001

EXTENSIONS

Definition corrected by Alexandre Wajnberg, Aug 31 2005

STATUS

approved

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Last modified October 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)