Palindromes and Antipalindromes in Short Intervals
Prapanpong Pongsriiam
Department of Mathematics
Faculty of Science
Silpakorn University
Nakhon Pathom 73000
Thailand
Kota Saito
Faculty of Pure and Applied Sciences
University of Tsukuba
1-1-1 Tennodai, Tsukuba
Ibaraki, 305-8577
Japan
Abstract:
For each positive integer b larger than 1, 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.
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(Concerned with sequences
A002113
A002385
A035928.)
Received July 19 2023; revised version received December 6 2023.
Published in Journal of Integer Sequences,
December 11 2023.
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