Nim is a two-player impartial game, played with piles of stones. On a player's turn, he or she chooses a pile and removes one or more stones from it. The player who takes the last stone is the winner. Nuclear nim (not a standard name) has the same rules as nim, but with one additional move: on a player's turn, he or she may choose to remove all of the remaining stones. Of course the first player has a winning strategy in any non-empty game of nuclear nim.
Is there a formula for the nimber of a position in nuclear nim? I am particularly interested in the case when there are just two piles. The nimbers can certainly be computed recursively, but I am hoping there is non-recursive expression (as there is for classical nim). I computed a table of values in the two-pile case, but I could not discern a pattern, and already the third row is not in Sloane's database.