The base ten integer 839 has the representations 1132 and 11324 respectively in base 9 and base 5. Accordingly, 839 has a base 5 representation that begins with its base 9 representation.

For which other base ten integers between 10 and 2014 inclusively do the base 5 representation of the integer begin with its base 9 representation?

(In reply to Simpler computer solution by Jer)

As usual I wanted to go beyond the artificial limit of 2014, and found the interesting result that there were no more solutions than these, even considering numbers up to 200,000 decimal. And in fact there are no more examples even up to 2,000,000.

Edited on May 27, 2014, 1:09 pm

Posted by Charlie on 2014-05-27 13:06:02