A b-palindrome is an integer that is a palindrome in base

*b*.

Show how to find a number that is a b-palindrome, of at least three digits, for at least *1000* different values of b.

*For example, 200 is not a 10-palindrome, but it is a 9-palindrome (242) and a 7-palindrome (404).*

The number 2^(1002!) is a perfect power with bases 2^2=4, 2^3=8, 2^4=16, . . . . 2^1000, 2^1001, 2^1002.

Then, the number 2^(1002!)+1 is a palindrome of at least three digits in bases 2^2=4, 2^3=8, 2^4=16, . . . . 2^1000, 2^1001, 2^1002. All of the palindromes begin with a '1', end with a '1' and all the digits in between are zeros.

Can anyone come up with a smaller number?

*Edited on ***February 25, 2004, 3:03 pm**