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).

1596591942865920001 = 21! / 32 + 1 is palindromic in over 1016 bases. I say over, because of the size of the number. It takes a long time to check every base up to the sqrt(x), and so I only check the values in the range sqrt(x/2) to sqrt(x), and of those, only the ones that are factors of (x-1) are bases that x is palindromic in. 

Edited on April 6, 2006, 9:36 am

Posted by Justin on 2006-04-04 10:19:04