A074313 -id:A074313 - cp's OEIS frontend

A110056 Least prime that ends a complete Cunningham chain (of the first kind) of length n.

13, 7, 167, 4079, 47, 2879, 71850239, 2444789759, 21981381119, 13357981992959, 681004115066879, 1136001594224639, 16756459239477534719, 781558105952602767359

Offset: 1

Alexandre Wajnberg, Sep 04 2005

"Complete" means that this chain is not part of a longer Cunningham chain of the first kind.
Next term is greater than 4*10^17.
A005602(13)-> 8181864863026139 -> ... -> a(13) = 16756459239477534719. [From Washington Bomfim, Oct 21 2009]

			41->83->167 is a Cunningham chain of the first kind. It is complete because neither (41-1)/2 nor 2*167+1 is prime. It is the first such chain of three primes, so a(3) = 167.

Chris Caldwell's Prime Glossary, Cunn ingham chains.

Cf. A005384, A005385, A007700, A023272, A023302, A023330, A059452, A057326, A059455, A059761, A059762, A059763, A059764, A074313.
Cf. A110059 for Cunningham chains of the second kind.
Cf. A005602 [From Washington Bomfim, Oct 21 2009]

Edited and extended by David Wasserman, Aug 08 2006

a(13) and a(14) from Washington Bomfim, Oct 21 2009

A095750 "Degree" of the Sophie Germain primes (A005384).

Original entry on oeis.org

0, 0, 1, 2, 3, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0

Offset: 0

Andrew S. Plewe, Jul 09 2004

This sequence is derived from the special case of Cunningham chains of the first kind where every member of the chain is a Sophie Germain prime.

This sequence can be obtained by subtracting 2 from A074313 and then deleting all negative members. - David Wasserman, Sep 13 2007

			Entries 0, 0, 1, 2, 3 correspond to the Sophie Germain primes 2, 3, 5, 11, 23. 5 is degree 1 because 5 = (2 * 2) + 1 and 2 is also a Sophie Germain prime. Similarly, 11 = (5 * 2) + 1, therefore 11 is degree 2. 23 = (11 * 2) + 1, thus 23 is degree 3 and so on.

C. K. Caldwell, Cunningham Chains.
Eric Weisstein's World of Mathematics, Cunningham Chain.

Cf. A005384.

More terms from David Wasserman, Sep 13 2007

cp's OEIS Frontend

A110056 Least prime that ends a complete Cunningham chain (of the first kind) of length n.

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