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Pongsriiam, Prapanpong; Saito, Kota

Palindromes and antipalindromes in short intervals. (English) Zbl 1532.11020

J. Integer Seq. 26, No. 9, Article 23.9.5, 28 p. (2023).
Summary: 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.

MSC:

11A63 Radix representation; digital problems
11J72 Irrationality; linear independence over a field

Keywords:

palindrome; antipalindrome; gap; digital problem; irrationality

Software:

OEIS
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References:

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[16] Mathematics Subject Classification: Primary 11A63; Secondary 11B05, 11J72. Keywords: palindrome, antipalindrome, gap, digital problem, irrationality. (Concerned with sequences A002113, A002385, and A035928.)
[17] Received July 19 2023; revised version received December 6 2023. Published in Journal of Integer Sequences, December 11 2023. Return to Journal of Integer Sequences home page.
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