On Fri, 31 Dec 2010 10:15:27 -0800, Ben Pfaff wrote:
> (Richard Harter) writes:
>
>> Are there any numbers that are not palindromes in any base, with the
>> proviso that the palindrome must have at least two "digits"? If so,
>> which is the smallest?
>
> I think that 2 is the smallest, because it is not a palindrome in base
> 2, and with bases higher than 2 it has only one digit.
But 2 is a palindrome in base 1. Indeed, every number n>1 is
a palindrome in base 1 and in base n-1, so if n>1, n is not a
number that is not a palindrome in any base. However, no number
that is preceded by a minus sign is a palindrome in a
number system with a positive base.
--
jiw