MathDB

A positive integer

x

k

-equivocal if there exists two positive integers

b

b'

such that when

x

is represented in base

b

and base

b'

, the two representations have digit sequences of length

k

that are permutations of each other. The smallest

2

-equivocal number is

7

, since

7

21

in base

3

and

12

in base

5

. Find the smallest

3

-equivocal number.

7