What is the name of the following combinatorial game:


Two players, moving in turn.


Positions: $0,1,2,\ldots$.


Moves: $n\longmapsto n-1$ or $n\longmapsto \lfloor n/2\rfloor$
if $n>0$.


No move for $0$ which loses.


The determination of the winning strategy is easy:
$n=2^k(2m+1)>0$ wins if and only if $k$ is even.


Determinating the winning strategy for the misere convention ($0$ wins) is also easy:


$2^k$ wins for $k$ odd and loses for $k$ even,


$2^k(2m+1)$ with $m\geq 1$ wins for $k$ even and loses for $k$ odd.


This game has certainly been described somewhere. Does it has a name? Does somebody have a reference?



Name for an easy combinatorial game
This is "Mark", supposedly due to Mark Krusemeyer; see the first sentence of the introduction to <https://arxiv.org/abs/1509.04199> and section 2 of <https://doi.org/10.37236/2015>.


