A368878 a(n) is the least k such that A368877^k(n) < n or -1 if no such k exists.

2, 1, 1, 2, 3, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 2, 8, 1, 2, 1, 1, 1, 1, 1, 2, 1, 8, 1, 2, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 7, 7, 1, 2, 1, 2, 2, 2, 8, 8, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 7, 7, 1, 1, 1, 1, 1, 1, 1, 6, 1

Offset

3,1

Comments

This is the falling time function ft in the paper of Eliahou et al.

The offset is 3 because A368877(1) = A368877(2) = 2, so for n<3 is not defined.

Links

Paolo Xausa, Table of n, a(n) for n = 3..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]];
A368878[n_]:=Length[NestWhileList[A368877, n, #>=n&]]-1;
Array[A368878, 120, 3] (* Paolo Xausa, Jan 08 2024 *)

Prog

(PARI) T(n) = if (n%2, (3*n+1)/2, n/2); \\ A014682
jp(n) = my(N=1+logint(n, 2)); for (i=1, N, n = T(n)); n; \\ A368877
a(n) = my(k=1, m=n); while ((m=jp(m)) >= n, k++); k;

Crossrefs

Cf. A014682, A070939, A368877.

Sequence in context: A161789 A109671 A141289 * A284271 A241915 A301891

Adjacent sequences: A368875 A368876 A368877 * A368879 A368880 A368881

Keyword

nonn

Author

Michel Marcus, Jan 08 2024

Status

approved