Introduction

A few years ago I dreamed of a number whose continued fraction digits and decimal digits were identical. Once awake, I could not remember the digits of the number. So I tried to re-create the number (if such a number even exists) with Mathematica. I found that such a number (and even more than one) seems to exist.

In this Corner, we will implement a search program that looks for such numbers. All of the following will be purely experimental; I have not been able to prove existence, uniqueness, or any properties of these numbers.