A111145 Length of the Cunningham chain initiated by the n-th Sophie Germain prime.

5, 2, 4, 3, 2, 2, 3, 2, 2, 6, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 4, 2, 4, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2

Offset: 1

Author

Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Oct 18 2005

Keywords

• nice
• nonn

Comments

If a(n) is a high-water mark of this sequence, then A057331(a(n)) is the first term of the first Cunningham sequence of length a(n). For example, a(10)=6 is a high-water mark of this sequence and A057331(a(10))=89 is the first term of the first Cunningham sequence of length 6.

Examples

			a(10)=6 because 89, the 10th Sophie Germain prime, is the first term of the Cunningham chain 89, 179, 359, 719, 1439, 2879, which consists of 6 terms.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005384, A057331.

Programs

Mathematica

lst=Select[Prime[Range[1000]], PrimeQ[2#+1]&]; Table[p=lst[[i]]; k=1; While[p=2p+1; PrimeQ[p], k++ ]; k, {i,Length[lst]}] (* T. D. Noe, Jun 06 2006 *)
ccl[n_]:=Length[NestWhileList[2#+1&,n,PrimeQ[2#+1]&]]; ccl/@Select[ Prime[ Range[1000]],PrimeQ[2#+1]&] (* Harvey P. Dale, Sep 29 2018 *)

Extensions

More terms from T. D. Noe, Jun 06 2006