# Name for an easy combinatorial game

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?