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
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