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.

(In reply to computer solution by Charlie)

I see a pattern.  Excluding the 300.  Each trio of bases starts where the last one ends.  6-7-8, 8-9-10, 10-11-12 etc.  I don't have time to investigate.  Does it continue or just coincidence?

Posted by Jer on 2013-12-04 18:27:49