cp's OEIS Frontend

A005603 Smallest prime beginning a complete Cunningham chain (of the second kind) of length n.

%I A005603 M4766 #30 Jul 08 2025 16:31:59
%S A005603 11,7,2,2131,1531,385591,16651,15514861,857095381,205528443121,
%T A005603 1389122693971,216857744866621,758083947856951,107588900851484911,
%U A005603 69257563144280941,3203000719597029781
%N A005603 Smallest prime beginning a complete Cunningham chain (of the second kind) of length n.
%C A005603 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 A005603 According to Augustin's web site, the numbers 107588900851484911, 69257563144280941, 3203000719597029781 are also in the sequence. - _Dmitry Kamenetsky_, May 14 2009
%D A005603 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005603 Dirk Augustin, <a href="http://primerecords.dk/Cunningham_Chain_records.htm">Cunningham Chain records</a>.
%H A005603 C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=CunninghamChain">Cunningham chain</a>.
%H A005603 G. Löh, <a href="http://www.jstor.org/stable/2008735">Long chains of nearly doubled primes</a>, Math. Comp., 53 (1989), 751-759.
%Y A005603 See A064812 for another version.
%Y A005603 Cf. (A005382 and A005383), A057326, A057327, A057328, A057329, A057330, A057331, A005602.
%K A005603 nonn,more
%O A005603 1,1
%A A005603 _N. J. A. Sloane_
%E A005603 6th term corrected from 385591 on Feb 23 1995, at _Robert G. Wilson v_'s suggestion
%E A005603 a(14) and a(15) found by Paul Jobling (Paul.Jobling(AT)WhiteCross.com) [Oct 23 2000]
%E A005603 a(6) reverted to original value by _Sean A. Irvine_, Jul 10 2016
%E A005603 a(16) from Augustin's page, comment corrected by _Jens Kruse Andersen_, Jun 14 2014
%E A005603 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 A005603 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