The Brussels choice, also called Choix de Bruxelles, replaces a positive integer by doubling or halving a selected part of its decimal
expansion. Choose a nonempty contiguous digit block
whose first digit is nonzero, and let 
be the integer it represents.
Replace the block in place by the decimal expansion
of 
,
or by that of 
if 
is an even number. Leaving the input unchanged is
also allowed (Angelini et al. 2019, p. 195).
For example, applying the rule to 16 gives exactly 8, 13, 16, 26, 32, 112, which is row 16 of OEIS A323460 (Angelini et al. 2019, p. 196).
The operation is reversible. The undirected graph whose vertices are the positive integers, with an graph edge joining distinct values obtainable from each other in one step, has exactly two connected components. They consist respectively of the positive integers divisible by 5 and those not divisible by 5 (Angelini et al. 2019, pp. 197-198).
Starting from 1, the minimum numbers of steps needed to reach the targets 1, 2, 3, ... are 0, 1, 11, 2, -1, 10, 9, 3, 9, -1, ... (OEIS A323454), where -1 denotes an unreachable target (Angelini et al. 2019, p. 198).
