A379148 a(n) is the number of iterations of the function x --> 2*x + 1 such that x remains prime, starting from A005384(n).

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, 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, 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

Offset: 1

Author

Ctibor O. Zizka, Dec 16 2024

Keywords

• nonn

Comments

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.

Examples

			n = 1: A005384(1) = 2 --> 5 --> 11 --> 23 --> 47 --> 95, 95 is not a prime, thus a(1) = 4.
n = 2: A005384(2) = 3 --> 7 --> 15, 15 is not a prime, thus a(2) = 1.
		

Crossrefs

Cf. A000040, A005384, A005385, A371980.

Programs

Mathematica

s[n_] := -2 + Length[NestWhileList[2*# + 1 &, n, PrimeQ[#] &]]; Select[Array[s, 5000], # > 0 &] (* Amiram Eldar, Dec 16 2024 *)

Formula

a(A371980(n)) = 1.