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, zerofree continued fraction representation and its radix representation.
Notebook
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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
