Find a number X such that "prepending" 4 to X equals to 4 times the number generated by "suffixing" X with 4

findNumber.pl

%% Find a number X such that "prepending" 4 to X equals to
%% 4 times the number generated by "suffixing" X with 4.
%%
%% X = X1,...,Xn . 4,X1,...,Xn = 4 * X1,...Xn,4
%%
%% :- find( 4, 9000, 11000, N ).
%%

natural( 0 ).
natural( s(X) ) :- natural( X ).

leq( 0, X ) :- natural( X ).
leq( s(X), s(Y) ) :- leq( X, Y ).

numbToPeano( 0, 0 ).
numbToPeano( N, s(X) ) :-
  N > 0,
  M is N - 1,
  numbToPeano( M, X ).

peanoToNumb( 0, 0 ).
peanoToNumb( s(X), N ) :-
  peanoToNumb( X, M ),
  N is M + 1.

digits( X, 1 ) :- X =< 9.
digits( X, D ) :-
  X > 9,
  X1 is X // 10,
  digits( X1, D1 ),
  D is D1 + 1.

generateNumber( InfLimit, SupLimit, N ) :-
  numbToPeano( SupLimit, SupLimitPeano ),
  numbToPeano( InfLimit, InfLimitPeano ),
  leq( Peano, SupLimitPeano ),
  leq( InfLimitPeano, Peano ),
  peanoToNumb( Peano, N ).

find( C, InfLimit, SupLimit, N ) :-
  generateNumber( InfLimit, SupLimit, N ),
  digits( N, D ),
  CN is N + C * 10**D,
  NC is 10 * N + C,
  CN =:= C * NC.