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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. 0
11, 3, 2, 509, 2, 89, 16651, 15514861, 85864769, 26089808579, 665043081119, 554688278429, 758083947856951 (list; graph; refs; listen; history; text; internal format)



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.


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

Chris Caldwell's Prime Glossary, Cunningham chains.


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


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.


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




Alexandre Wajnberg, Sep 04 2005


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



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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)