The game Officers

In the book "Winning Ways" by Berlekamp, Conway, Guy (aka the bible of combinatorial game theory) there is a short section about the game Officers in Chapter 4. It has also the symbolical name $\cdot {\bf 6}$. Its Grundy function is given by

$G(n) := mex(\{G(a) \oplus G(n-1-a)\} : 1 \leq a \leq n\}$,

where $\oplus$ is the nim-sum. This is the OEIS sequence A046695, where you also find some values. It is noted that this sequence has "a strong inclination towards a period of $26$", but that "a complete analysis is still to be found".