cp's OEIS Frontend

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.

%I A110089 #22 Sep 03 2024 23:03:25
%S A110089 11,3,2,509,2,89,16651,15514861,85864769,26089808579,665043081119,
%T A110089 554688278429,758083947856951,95405042230542329,69257563144280941
%N 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.
%C A110089 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.
%H A110089 Chris Caldwell's Prime Glossary, <a href="https://t5k.org/glossary/page.php?sort=CunninghamChain">Cunningham chains</a>.
%F A110089 a(n) = min(A005602(n), A005603(n)). - _R. J. Mathar_, Jul 23 2008
%e A110089 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>.
%e A110089 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>).
%e A110089 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.
%Y A110089 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.
%K A110089 nonn,more,hard
%O A110089 1,1
%A A110089 _Alexandre Wajnberg_, Sep 04 2005
%E A110089 a(8)-a(13) via A005602, A005603 from _R. J. Mathar_, Jul 23 2008
%E A110089 a(14)-a(15) via A005602, A005603 from _Jason Yuen_, Sep 03 2024