# Documentation

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## Sequences of Numbers

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

### Fibonacci Numbers

The Fibonacci numbers are a sequence of integers. The following recursion formula defines the `n`th 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.