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

1,1

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.

Links

Table of n, a(n) for n=1..99.

Formula

a(A371980(n)) = 1.

Example

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.

Mathematica

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

Crossrefs

Cf. A000040, A005384, A005385, A371980.

Sequence in context: A368922 A327357 A386234 * A334810 A348566 A021246

Adjacent sequences: A379145 A379146 A379147 * A379149 A379150 A379151

Keyword

nonn

Author

Ctibor O. Zizka, Dec 16 2024

Status

approved