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

• Published in 2009
In the collections
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.

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}
}