On N-Continued Fractions of Quadratic Irrationality (Very Temporary Title)

On N-Continued Fractions of Quadratic Irrationality (Very Temporary Title)

By
Robert Dogherty-Bliss, Nathan Fox and Doron Zeilberger
.pdf .ps .tex

First VersionWritten: Jan. 1, 2015;
Renewed (with RDB on board): April 2020
So far this page is only a place-holder to document the software and its output.

Maple Package

NCF.txt: a Maple package to study N-continued fractions, and especially those of quadratic irrationalities

Some Input and Output files for the Maple package NCF

If you want to see the first 100000 terms of the 7-continued fraction of 3^1/2, and find out that no period is detected so far,
the input yields the output

If you want to see the 1-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of non-perfect-square positive integers from 2 to 9999,
the input yields the output

If you want to see the 1-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of all the first 1000 primes
the input yields the output

If you want to see the 2-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of non-perfect-square positive integers from 2 to 2499,
the input yields the output

If you want to see the 2-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of all the first 200 primes
the input yields the output

If you want to see the 3-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of non-perfect-square positive integers from 2 to 2499,
the input yields the output

If you want to see the 3-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of all the first 200 primes
the input yields the output

If you want to see the 4-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of non-perfect-square positive integers from 2 to 2499,
the input yields the output

If you want to see the 4-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of all the first 200 primes
the input yields the output

If you want to see the 5-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of non-perfect-square positive integers from 2 to 2499,
the input yields the output

If you want to see the 5-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of all the first 200 primes
the input yields the output

If you want to see the 6-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of non-perfect-square positive integers from 2 to 2499,
the input yields the output

If you want to see the 6-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of all the first 200 primes
the input yields the output

If you want to see the 7-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of non-perfect-square positive integers from 2 to 2499,
the input yields the output

If you want to see the 7-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of all the first 200 primes
the input yields the output

If you want to see the 8-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of non-perfect-square positive integers from 2 to 2499,
the input yields the output

If you want to see the 8-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of all the first 200 primes
the input yields the output

If you want to see the 9-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of non-perfect-square positive integers from 2 to 2499,
the input yields the output

If you want to see the 9-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of all the first 200 primes
the input yields the output

If you want to see the 10-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of non-perfect-square positive integers from 2 to 2499,
the input yields the output

If you want to see the 10-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of all the first 200 primes
the input yields the output

If you want to see the 11-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of non-perfect-square positive integers from 2 to 2499,
the input yields the output

If you want to see the 11-continued fractions that are ultimately periodic by looking at the first 2000 terms for all square-roots of all the first 200 primes
the input yields the output

Doron Zeilberger's Home Page