Finding Trott Constants
Michael Trott · The Mathematica Journal · 2006
A Trott constant is a number whose continued fraction representation (simple or not) is the same as the digits of its radix representation. For instance, in base 10, 0.1084101... = 0 + 1 / (1 + 1 / (0 + 1 / (8 + 1 / (4 + 1 / (1 + 1 / (0 + 1 / (1 ...))))))). This Corner implements a search method for such numbers and lists its results. The best number we found has more than 400 digits in common between its nonsimple, zero-free continued fraction representation and its radix representation.