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Palindromes in Different Bases: A Conjecture of J. Ernest Wilkins

Veröffentlicht/Copyright: 26. Januar 2010
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Integers
Aus der Zeitschrift Band 9 Heft 6

Abstract

We show that there exist exactly 203 positive integers N such that for some integer d ≥ 2 this number is a d-digit palindrome base 10 as well as a d-digit palindrome for some base b different from 10. To be more precise, such N range from 22 to 9986831781362631871386899.

Keywords.: Palindrome
Received: 2009-04-26
Accepted: 2009-10-13
Published Online: 2010-01-26
Published in Print: 2009-December

© de Gruyter 2009

Artikel in diesem Heft

  1. On the Complexity of n-Player Hackenbush
  2. On the Equation ax ≡ x (mod b)
  3. A New Generalization of Fibonacci Sequence & Extended Binet's Formula
  4. On Rainbow Solutions to an Equation with a Quadratic Term
  5. 2-Pile Nim with a Restricted Number of Move-Size Imitations
  6. The Finite Heine Transformation and Conjugate Durfee Squares
  7. A Short Note on the Difference Between Inverses of Consecutive Integers Modulo p
  8. Factorization Results with Combinatorial Proofs
  9. Squares in (12 + m2) ⋯ (n2 + m2)
  10. On Monochromatic Sets of Integers Whose Diameters Form a Monotone Sequence
  11. Palindromes in Different Bases: A Conjecture of J. Ernest Wilkins
  12. Une forme effective d'un théorème de Bateman sur la fonction phi d'Euler
  13. Differences of Multiple Fibonacci Numbers
https://doi.org/10.1515/INTEG.2009.059
Schlagwörter für diesen Artikel
Palindrome

Artikel in diesem Heft

  1. On the Complexity of n-Player Hackenbush
  2. On the Equation ax ≡ x (mod b)
  3. A New Generalization of Fibonacci Sequence & Extended Binet's Formula
  4. On Rainbow Solutions to an Equation with a Quadratic Term
  5. 2-Pile Nim with a Restricted Number of Move-Size Imitations
  6. The Finite Heine Transformation and Conjugate Durfee Squares
  7. A Short Note on the Difference Between Inverses of Consecutive Integers Modulo p
  8. Factorization Results with Combinatorial Proofs
  9. Squares in (12 + m2) ⋯ (n2 + m2)
  10. On Monochromatic Sets of Integers Whose Diameters Form a Monotone Sequence
  11. Palindromes in Different Bases: A Conjecture of J. Ernest Wilkins
  12. Une forme effective d'un théorème de Bateman sur la fonction phi d'Euler
  13. Differences of Multiple Fibonacci Numbers
Heruntergeladen am 13.5.2026 von https://www.degruyterbrill.com/document/doi/10.1515/INTEG.2009.059/html?lang=de
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