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Volume 10, Issue 2

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T R O T T ' S   C O R N E R
Finding Trott Constants
Michael Trott

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.

*Notebook


*PDF


*HTML

*Introduction

*Existing Sequences

*Some Formatting Functions

*Difference Between Continued Fractions and Radix Forms

*Investigating Small Sequences

*Search Function for the Constants

*Carrying Out and Monitoring Searches

*Some Constants That Were Found

*Digit Gains with Seeded Sequences

*Why Searches Are Difficult

*Summary

*References

*Additional Material

Michael Trott
Senior Member,
Technical Staff
Wolfram Research, Inc.
mtrott@wolfram.com


     
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