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Volume 10, Issue 2


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

Difference Between Continued Fractions and Radix Forms

The next two functions construct a rational number (an integer in degenerate cases) from the lists of digits.

To measure the quality of a Trott constant, we compare the value of the radix form and the continued fraction. The function radixCFDifference calculates the difference.

Here again are two examples.

The function numberOfCoincidingDigits calculates the number of coinciding digits in the continued fraction and base decimal representation (including the leading zero).

Here are our two examples.

Here we analyze the three sequences from the integer database.

We define another function for later use. Given a sequence, the function shortenedSequence shortens it to the minimal length that exhibits the maximal number of coinciding digits.

Here a continuation of the sequence (which does not improve) is shortened to its optimal length.

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