A certain 10-base integer with distinct digits can be converted to base b by merely reversing its digits.
Find the lowest value of b.

The smallest value for b would be 4.

The following is a list of base-10 numbers of two or more digits where each digit is distinct within its number and where there exists a reversal in a different base. The list excludes those numbers where the base-10 number ends with a zero, as a reversal then would have a leading zero.
   13   =   31₄
   23   =   32₇
   46   =   64₇
   43   =   34₁₃
   86   =   68₁₃
  834   =  438₁₄
   53   =   35₁₆
  371   =  173₁₆
   21   =   12₁₉
   42   =   24₁₉
   63   =   36₁₉
   84   =   48₁₉
 9471   = 1749₁₉
  912   =  219₂₁
   73   =   37₂₂
   83   =   38₂₅
   31   =   13₂₈
   62   =   26₂₈
   93   =   39₂₈
  961   =  169₂₈
   41   =   14₃₇
   82   =   28₃₇
   51   =   15₄₆
   61   =   16₅₅
   71   =   17₆₄
   81   =   18₇₃
   91   =   19₈₂

Posted by Dej Mar on 2011-03-30 13:15:20