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

Author

Michel Marcus, Jan 08 2024

Keywords

• nonn

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.

Crossrefs

Cf. A014682, A070939, A368878.

Programs

Mathematica

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

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;