OFFSET
1,3
COMMENTS
This sequence is a variant of "Choix de Bruxelles" (where we consider substring substitutions of the form k <-> 2*k, see A323286):
- we map a positive number n to any number that can be obtained as follows:
- take a nonempty substring s (without leading zero) in the decimal representation of n,
- if the value of s corresponds to an even number, replace s by s/2,
- otherwise replace s by 3*s + 1.
The sequence is well defined:
- the proof is similar to that described in A337321,
- the initial paths to consider here are the following:
1
2 -> 1
3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
4 -> 2 -> 1
5 -> 16 -> 8 -> 4 -> 2 -> 1
6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
7 -> 22 -> 11 -> 34 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1
8 -> 4 -> 2 -> 1
9 -> 28 -> 24 -> 22 -> 21 -> 64 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1
10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
11 -> 34 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..3652
Rémy Sigrist, PARI program for A337357
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist and N. J. A. Sloane, Aug 24 2020
STATUS
approved