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

1,1

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A005384, A057331.

Sequence in context: A372286 A368690 A083241 * A249920 A021660 A266122

Adjacent sequences: A111142 A111143 A111144 * A111146 A111147 A111148

Keyword

nice,nonn

Author

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

Extensions

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

Status

approved