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Sequences of Numbers

Fibonacci Numbers

The Fibonacci numbers are a sequence of integers. The following recursion formula defines the nth Fibonacci number:

To compute the Fibonacci numbers, use the numlib::fibonacci function. For example, the first 10 Fibonacci numbers are:

numlib::fibonacci(n) $ n = 0..9

Mersenne Primes

The Mersenne numbers are the prime numbers 2p - 1. Here p is also a prime. The numlib::mersenne function returns the list that contains the following currently known Mersenne numbers:

numlib::mersenne()

Continued Fractions

The continued fraction approximation of a real number r is an expansion of the following form:

Here a1 is the integer floor(r), and a2, a3, ... are positive integers.

To create a continued fraction approximation of a real number, use the numlib::contfrac function. For example, approximate the number 123456/123456789 by a continued fraction:

numlib::contfrac(123456/123456789)

Alternatively, you can use the more general contfrac function. This function belongs to the standard library. While numlib::contfrac accept only real numbers as parameters, contfrac also accepts symbolic expressions. When working with real numbers, contfrac internally calls numlib::contfrac, and returns the result of the domain type numlib::contfrac:

a := contfrac(123456/123456789);
domtype(a)

Since contfrac internally calls numlib::contfrac, calling the numlib::contfrac directly can speed up your computations.

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