Palindromes and Antipalindromes in Short Intervals

For each positive integer rblargerthan1, we obtain the shortest intervals that always contain a b-adic palindrome and a b-adic antipalindrome. We also give some results on the classification of b-adic twin palindromes, gaps that occur infinitely often between b-adic palindromes, and the irrationality of the sum of reciprocals of a particular type of b-adic palindrome.