Abstract
Palindromic numbers have intrigued amateur mathematicians and number theorists alike. Initially regarded as recreational mathematics, these numbers have been extensively explored and are well-documented in the On-Line Encyclopedia of Integer Sequences (OEIS). Within the last few decades, an exhaustive list of sequences has been compiled regarding palindromic numbers, notably palindromic primes and appended palindromic numbers. Both palindromic primes and appended palindromic numbers have been well-studied within bases 2-10, yet are poorly documented in larger bases. To extend the literature on appended palindromic numbers, a novel algorithm is proposed that computes sequences of primes with prime mirrors in bases 2-62, resulting in 52 novel sequences. A second algorithm is proposed that computes the list of primes that require an additional base to obtain a prime mirror, providing yet another novel sequence.
Highlights
Palindromes have captivated linguists for centuries with analyses dating back to Henry Peacham’s thesis in 1643 [1]
To contribute to the blossoming list of palindrome-related sequences, this paper proposes a novel algorithm which has discovered sequences of primes with prime mirrors throughout bases 11-62
If the converted mirror is prime, we found a pair of prime numbers that form an appended palindromic numbers (APNs) in the current base
Summary
Palindromes have captivated linguists for centuries with analyses dating back to Henry Peacham’s thesis in 1643 [1]. To contribute to the blossoming list of palindrome-related sequences, this paper proposes a novel algorithm which has discovered sequences of primes with prime mirrors throughout bases 11-62. The main contribution of this paper is the Smaug sequence, which contains the prime numbers that require the use of an additional base to have a prime mirror.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Advanced Research in Computer Science
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
