Find palindromic numbers in both binary and ternary bases

You are encouraged to solve this task according to the task description, using any language you may know.
Task

   Find and show (in decimal) the first six numbers (non-negative integers) that are   palindromes   in   both:
   base 2
   base 3
   Display   0   (zero) as the first number found, even though some other definitions ignore it.
   Optionally, show the decimal number found in its binary and ternary form.
   Show all output here.


It's permissible to assume the first two numbers and simply list them.



See also
   Sequence A60792,   numbers that are palindromic in bases 2 and 3 on The On-Line Encyclopedia of Integer Sequences.


with Ada.Text_IO, Base_Conversion;
 
procedure Brute is
 
   type Long is range 0 .. 2**63-1;
   package BC is new Base_Conversion(Long);
 
   function Palindrome (S : String) return Boolean is
      (if S'Length < 2 then True
      elsif S(S'First) /= S(S'Last) then False
      else Palindrome(S(S'First+1 .. S'Last-1)));
 
   function Palindrome(N: Long; Base: Natural) return Boolean is
      (Palindrome(BC.Image(N, Base =>Base)));
 
  package IIO is new Ada.Text_IO.Integer_IO(Long);
 
begin
   for I in Long(1) .. 10**8 loop
      if Palindrome(I, 3) and then Palindrome(I, 2) then
	 IIO.Put(I, Width => 12); -- prints I (Base 10)
	 Ada.Text_IO.Put_Line(": " & BC.Image(I, Base => 2) & "(2)" &
			      ", " & BC.Image(I, Base => 3) & "(3)");
	 -- prints I (Base 2 and Base 3)
      end if;
      end loop;
end Brute;