Help:=proc(): print(`IsLosing(k), LosingList(N)`): end:


#IsLosing(k): In the Alice-Bob game
#where a legal move consists of either
#removing 1 penny or trunc(k/2) pennies
#is the position losing?

IsLosing:=proc(k) 
option remember:

if k=0 then
 RETURN(true):
fi:

if not IsLosing(k-1) and not IsLosing(trunc((k+1)/2)) then
  RETURN(true):
else
  RETURN(false):
fi:

end:

#LosingList(N): all the losing positions up to N pennies
LosingList:=proc(N) local L,i:

L:=[]:
for i from 0 to N do
 if IsLosing(i) then
  L:=[op(L),i]:
 fi:
od:

L:

end: