Palindromes in a base less than the square root

[Dr. Gordon Hamilton]

A100563 reports the number of times that a number is a palindrome in a base 
less than its square root.

For example 100 is a palindrome in bases 3, 7, and 9 so F(100) =3.

Are there an infinite number of "unkempt" numbers with F(n) = 0 ?

Thanks for any insight...

Gordon 



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