A110089 Smallest prime beginning (through <*2+1> or/and <*2-1>) a complete Cunningham chain (of the first or the second kind) of length n.

11, 3, 2, 509, 2, 89, 16651, 15514861, 85864769, 26089808579, 665043081119, 554688278429, 758083947856951

Offset

1,1

Comments

The word "complete" indicates each chain is exactly n primes long for the operator in function (i.e. the chain cannot be a subchain of another one); and the first and/or last term may be involved in a chain of the other kind (i.e. the chain may be connected to another one). a(1)-a(8) computed by Gilles Sadowski.

Links

Table of n, a(n) for n=1..13.

Chris Caldwell's Prime Glossary, Cunningham chains.

Formula

a(n)= min (A005602(n), A005603(n)). - R. J. Mathar, Jul 23 2008

Example

a(1)=11 because 2, 3, 5 and 7 are included in longer chains than one prime long; and 11 (although included in a <2p+1> chain, has no prime connection through <2p-1>.
a(2)=3 because 3 begins (through 2p+1>) the first complete two primes chain: 3-> 7 (even if 3 and 7 are also part of two others chains, but through <2p-1>).
a(3)=2 because (although 2 begins also a five primes chain through <2p+1>) it begins, through <2p-1>, the first complete three primes chain encountered: 2->3->5.

Crossrefs

Cf. A023272, A023302, A023330, A005384, A005385, A059452, A059455, A007700, A059759, A059760, A059761, A059762, A059763, A059764, A059765, A038397, A104349, A091314, A069362, A016093, A014937, A057326, A110059, A110056, A110038, A059766, A110027, A059764, A110025, A110024, A059763, A110022, A109998, A109946, A109927, A109835, A005603.

Sequence in context: A140749 A010188 A309389 * A177415 A208091 A070695

Adjacent sequences: A110086 A110087 A110088 * A110090 A110091 A110092

Keyword

nonn

Author

Alexandre Wajnberg, Sep 04 2005

Extensions

a(8)-a(13) via A005602, A005603 from R. J. Mathar, Jul 23 2008

Status

approved