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%I #7 Dec 16 2024 14:42:30
%S 4,1,3,2,1,1,2,1,1,5,1,1,1,4,1,1,1,1,1,1,3,1,1,1,1,3,1,1,1,1,1,2,1,1,
%T 1,1,1,1,2,2,1,1,1,3,1,3,1,2,2,1,2,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,1,
%U 1,1,1,2,1,1,1,3,1,1,2,1,1,1,1,1,1,1,1,1,1,2,2,3,1,1,1,1,1,2,1
%N a(n) is the number of iterations of the function x --> 2*x + 1 such that x remains prime, starting from A005384(n).
%C Cunningham chain of the first kind of length i is a sequence of prime numbers (p_1, ..., p_i) such that p_(r + 1) = 2*p_r + 1 for all 1 =< r < i. This sequence tells the length of the Cunningham chain of the first kind for primes from A005384.
%F a(A371980(n)) = 1.
%e n = 1: A005384(1) = 2 --> 5 --> 11 --> 23 --> 47 --> 95, 95 is not a prime, thus a(1) = 4.
%e n = 2: A005384(2) = 3 --> 7 --> 15, 15 is not a prime, thus a(2) = 1.
%t s[n_] := -2 + Length[NestWhileList[2*# + 1 &, n, PrimeQ[#] &]]; Select[Array[s, 5000], # > 0 &] (* _Amiram Eldar_, Dec 16 2024 *)
%Y Cf. A000040, A005384, A005385, A371980.
%K nonn,new
%O 1,1
%A _Ctibor O. Zizka_, Dec 16 2024