A059688 Length of Cunningham chain containing prime(n) either as initial, internal or final term.

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, 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, 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

Offset: 1

Author

Labos Elemer, Feb 06 2001

Keywords

• nonn

Comments

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).

Examples

			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.
		

Links

• C. K. Caldwell, Cunningham Chains
• W. Roonguthai, Yves Gallot's Proth.exe and Cunningham Chains

Crossrefs

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

Extensions

Offset and a(5) corrected by Sean A. Irvine, Oct 01 2022