A059688 - OEIS

%I #13 Apr 03 2023 10:36:09

%S 5,2,5,2,5,0,0,0,5,2,0,0,3,0,5,2,2,0,0,0,0,0,3,6,0,0,0,2,0,2,0,2,0,0,

%T 0,0,0,0,3,2,6,0,2,0,0,0,0,0,2,0,2,2,0,2,0,2,0,0,0,2,0,2,0,0,0,0,0,0,

%U 2,0,0,6,0,0,0,2,0,0,0,0,2,0,2,0,0,2,0,0,0,0,2,2,0,2,0,2,4,0,0,0,0,0,2,0,0

%N Length of Cunningham chain containing prime(n) either as initial, internal or final term.

%C The length of a chain is measured by the total number of terms including the end points. a(n)=0 means that prime(n) is neither Sophie Germain nor a safe prime (i.e. it is in A059500).

%H C. K. Caldwell, <a href="https://t5k.org/glossary/page.php/CunninghamChain">Cunningham Chains</a>

%H W. Roonguthai, <a href="http://ksc9.th.com/warut/cunningham.html">Yves Gallot's Proth.exe and Cunningham Chains</a>

%e For all of {2,5,11,23,47}, i.e. at positions {j}={1,3,5,9,15} a(j)=5. Similarly for indices of all terms in {89,...,5759} a(i)=6. No chains are intelligible with length = 1 because the minimal chain enclose one Sophie Germain and also one safe prime. Dominant values are 0 and 2.

%Y Cf. A005384, A005385, A053176, A059452-A059456, A007700, A005602, A023272, A023302, A023330, A059500.

%K nonn

%O 1,1

%A _Labos Elemer_, Feb 06 2001

%E Offset and a(5) corrected by _Sean A. Irvine_, Oct 01 2022