Inserting elements into indexes that are the powers of 2 [Prolog]

Question

I have to insert an element into a list on the positions that are powers of 2

e.g. in the list

L = [1, 2, 3, 4, 5, 6, 7, 8] 

I should insert an element E = 0 after the first element, then the third, then the 7th, etc. so the resulting list would be

R = [1, 0, 2, 3, 0, 4, 5, 6, 7, 0, 8]

I tried using the predefined predicate nth1/4 to add an element into a list at a position P and then increase the position P by multiplying it with 2

%empty list
ins_aux(_, [], _, _, []).
%if the position is even, add the element and then multiply P by 2 
%and add a value K which is incremented at every step to get the next position 
ins_aux(E, L, P, K, Res) :- 0 is mod(P, 2), !, 
                         nth1(P, Res, E, L), 
                         P1 is (P*2)+K,
                         K1 is K+1,
                         ins_aux(E, Res, P1, K1, Res).
%if the position is odd, add the element to the list 
ins_aux(E, L, P, K, Res) :- nth1(P, Res, E, L),
                         P1 is P+1,
                         ins_aux(E, Res, P1, K, Res).

My issue is that this always outputs false. I am clearly doing something wrong it's just that I don't know what

Answer 1

Why use nth1 in ins_aux? This makes things ... unnecessarily quadratic:)

Here's how you could do it:

ins_aux([],_,_,[]).
ins_aux([E|Es],X,I,[E|Rs0]) :-
   (  I /\ (I-1) =\= 0
   -> Rs0 = Rs1                  % I is not a power of two
   ;  Rs0 = [X|Rs1]              % I is     a power of two
   ),
   I1 is I + 1,
   ins_aux(Es,X,I1,Rs1).

Sample queries using Scryer Prolog:

?- ins_aux([1,2,3,4,5,6,7,8],0,2,Rs).
   Rs = [1,0,2,3,0,4,5,6,7,0,8].

?- ins_aux([a,b,c,d,e,f,g,h],0,2,Rs).
   Rs = [a,0,b,c,0,d,e,f,g,0,h].