Interesting Esoterica

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

Article by Edray Herber Goins
  • Published in 2009
  • Added on
We show that there exist exactly 203 positive integers $N$ such that for some integer $d \geq 2$ 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.

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BibTeX entry

@article{PalindromesinDifferentBasesAConjectureofJErnestWilkins,
	title = {Palindromes in Different Bases: A Conjecture of J. Ernest Wilkins},
	abstract = {We show that there exist exactly 203 positive integers {\$}N{\$} such that for some
integer {\$}d \geq 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.},
	url = {http://arxiv.org/abs/0909.5452v1 http://arxiv.org/pdf/0909.5452v1},
	year = 2009,
	author = {Edray Herber Goins},
	comment = {},
	urldate = {2019-09-14},
	archivePrefix = {arXiv},
	eprint = {0909.5452},
	primaryClass = {math.NT},
	collections = {easily-explained,fun-maths-facts,integerology}
}