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

11, 7, 2, 2131, 1531, 385591, 16651, 15514861, 857095381, 205528443121, 1389122693971, 216857744866621, 758083947856951, 107588900851484911, 69257563144280941, 3203000719597029781

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

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.

According to Augustin's web site, the numbers 107588900851484911, 69257563144280941, 3203000719597029781 are also in the sequence. - Dmitry Kamenetsky, May 14 2009

References

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

Links

• Dirk Augustin, Cunningham Chain records.
• C. K. Caldwell, Cunningham chain.
• G. Löh, Long chains of nearly doubled primes, Math. Comp., 53 (1989), 751-759.

Crossrefs

See A064812 for another version.

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

Extensions

6th term corrected from 385591 on Feb 23 1995, at Robert G. Wilson v's suggestion

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

a(6) reverted to original value by Sean A. Irvine, Jul 10 2016

a(16) from Augustin's page, comment corrected by Jens Kruse Andersen, Jun 14 2014

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.

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