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Smallest prime beginning a complete Cunningham chain (of the second kind) of length n.
(Formerly M4766)
21

%I M4766 #26 Apr 03 2023 10:36:09

%S 11,7,2,2131,1531,385591,16651,15514861,857095381,205528443121,

%T 1389122693971,216857744866621,758083947856951,107588900851484911,

%U 69257563144280941,3203000719597029781

%N Smallest prime beginning a complete Cunningham chain (of the second kind) of length n.

%C The chain begins with a prime number p; next term p' (a prime) is produced forming 2p-1; next term p"=2p'-1, etc. "Complete" means that each chain is exactly n primes long (i.e. the chain cannot be a subchain of another one). That is why this sequence is slightly different from A064812, where the 6th term (33301) is smaller than here (385591) but is the second one of a seven primes sequence and therefore doesn't *start* a sequence.

%C According to Augustin's web site, the numbers 107588900851484911, 69257563144280941, 3203000719597029781 are also in the sequence. - _Dmitry Kamenetsky_, May 14 2009

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Dirk Augustin, <a href="http://primerecords.dk/Cunningham_Chain_records.htm">Cunningham Chain records</a>.

%H C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=CunninghamChain">Cunningham chain</a>.

%H G. Löh, <a href="http://www.jstor.org/stable/2008735">Long chains of nearly doubled primes</a>, Math. Comp., 53 (1989), 751-759.

%Y See A064812 for another version.

%Y Cf. (A005382 and A005383), A057326, A057327, A057328, A057329, A057330, A057331, A005602.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_.

%E 6th term corrected from 385591 on Feb 23 1995, at _Robert G. Wilson v_'s suggestion

%E a(14) and a(15) found by Paul Jobling (Paul.Jobling(AT)WhiteCross.com) [Oct 23 2000]

%E a(6) reverted to original value by _Sean A. Irvine_, Jul 10 2016

%E a(16) from Augustin's page, comment corrected by _Jens Kruse Andersen_, Jun 14 2014

%E Edited by _N. J. A. Sloane_, Nov 03 2018 at the suggestion of _Georg Fischer_, Nov 03 2018, merging a duplicate entry with this one.

%E In Augustin's web page there are 7 or so more terms which could be added here, or alternatively used to create a b-file. - _Georg Fischer_, Nov 03 2018