A111145 - OEIS

%I #10 Dec 21 2021 23:27:59

%S 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,

%T 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,

%U 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

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

%C 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.

%H T. D. Noe, <a href="/A111145/b111145.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t 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

%t ccl[n_]:=Length[NestWhileList[2#+1&,n,PrimeQ[2#+1]&]]; ccl/@Select[ Prime[ Range[1000]],PrimeQ[2#+1]&] (* _Harvey P. Dale_, Sep 29 2018 *)

%Y Cf. A005384, A057331.

%K nice,nonn

%O 1,1

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

%E More terms from _T. D. Noe_, Jun 06 2006