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 Consecutive Base Baffle (Posted on 2013-12-04)
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.

 No Solution Yet Submitted by K Sengupta No Rating

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 re: computer solution | Comment 2 of 4 |
(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

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