Determine the smallest positive integer which is a palindrome in precisely 3 consecutive bases (excluding base 10). What are the next two smallest positive integers with this property?
*** Any solution must have more than one digit in any given base. So, trivial solutions like (0)_{base 3}, (2)_{base 5} or, (C)_{base 14} are not allowed.
*** "Excluding base 10" means that the sequence of bases 9,11,12 for example, does not count as a possibility and, the bases have to be truly consecutive and all be on one side or the other of 10.