A379144 a(n) is the number of iterations of the function x --> 2*x - 1 such that x remains prime, starting from A005382(n).

2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1

Offset

1,1

Comments

Cunningham chain of the second 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 second kind for primes from A005382.

Links

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

Formula

a(A110581(n)) = 1.

a(A057326(n)) = 2.

Example

n = 1: A005382(1) = 2 --> 3 --> 5 --> 9, 9 is not a prime, thus a(1) = 2.
n = 3: A005382(3) = 7 --> 13 --> 25, 25 is not a prime, thus a(3) = 1.

Mathematica

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

Crossrefs

Cf. A000040, A005382, A005383, A057326, A064812, A110581, A307390.

Sequence in context: A348528 A307223 A321787 * A331596 A023586 A023584

Adjacent sequences: A379141 A379142 A379143 * A379145 A379146 A379147

Keyword

nonn

Author

Ctibor O. Zizka, Dec 16 2024

Status

approved