How can I get a list of the powers of X less-than or equal to N in Prolog?

Question

I am trying to learn more about prolog and I want to get a list of the powers of a certain number X less-than or equal to a number N. The result need to be something like this:

?- powers (5,123,List).
List = [25,5,1] ? ;
no

Thanks you so much!

Answer 1

powers(N, MaxP, Lst) :-
    % Start with empty list, to create list in descending order
    powers_(N, MaxP, 1, [], Lst).
    
powers_(N, MaxP, Upto, LstUpto, Lst) :-
    Upto =< MaxP,
    % Don't backtrack to the "finished" alternative
    !,
    Upto1 is Upto * N,
    % Loop, adding to list in reverse order
    powers_(N, MaxP, Upto1, [Upto|LstUpto], Lst).

% Finished - unify Lst
powers_(_N, _MaxP, _Upto, Lst, Lst).

Result in swi-prolog:

?- time(powers(5, 123, L)).
% 12 inferences, 0.000 CPU in 0.000 seconds (49% CPU, 216353 Lips)
L = [25,5,1].