A368877 a(n) = f^k(n) where f(n) = A014682(n), the Collatz map, and k = A070939(n), the length of n in base 2.

2, 2, 8, 2, 2, 8, 26, 2, 17, 2, 20, 8, 8, 26, 80, 2, 5, 17, 17, 2, 2, 20, 20, 8, 22, 8, 71, 26, 26, 80, 242, 2, 44, 5, 5, 17, 17, 17, 152, 2, 161, 2, 56, 20, 20, 20, 182, 8, 7, 22, 22, 8, 8, 71, 71, 26, 74, 26, 76, 80, 80, 242, 728, 2, 14, 44, 44, 5, 5, 5, 137, 17, 47, 17, 16

Offset

1,1

Comments

This is the jump function jp in the paper of Eliahou et al.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Shalom Eliahou, Jean Fromentin, and Rénald Simonetto, Is the Syracuse falling time bounded by 12?, hal-03294829, 2021.

Mathematica

A368877[n_] := Nest[If[OddQ[#], (3#+1)/2, #/2]&, n, IntegerLength[n, 2]];
Array[A368877, 100] (* Paolo Xausa, Jan 08 2024 *)

Prog

(PARI) T(n) = if (n%2, (3*n+1)/2, n/2); \\ A014682
a(n) = my(N=1+logint(n, 2)); for (i=1, N, n = T(n)); n;

Crossrefs

Cf. A014682, A070939, A368878.

Sequence in context: A365747 A344734 A037300 * A029623 A325753 A208133

Adjacent sequences: A368874 A368875 A368876 * A368878 A368879 A368880

Keyword

nonn

Author

Michel Marcus, Jan 08 2024

Status

approved