NAME

Math::Zeckendorf

Given an Int, generate the Zeckendorf decomposition of that number, or the Dual Zeckendorf decomposition.

SYNOPSIS

Return either the zeckendorf or the dual-zeckendorf decomposition. If :numbers is enabled, instead return the corresponding Fibonnaci numbers.

use Math::Zeckendorf;

say zeckendorf(27);
# OUTPUT: «[1 0 0 1 0 0 1]␤»

say zeckendorf(27, :numbers);
# OUTPUT: «[21 5 1]␤»

say dual-zeckendorf(27);
# OUTPUT: «[1 1 0 1 1 1]␤»

say dual-zeckendorf(27, :numbers);
# OUTPUT: «[13 8 3 2 1]␤»

DESCRIPTION

Inspired by the "Base Fibonacci" Numberphile video.

The binary digits returned from zeckendorf do not include any sequential Fibonacci numbers. See https://oeis.org/A014417

Conversely, the binary digits returned from dual-zeckendorf do not contain any gaps of Fibonacci numbers greater than size 1. See https://oeis.org/A104326

See also Zeckendorf's theorem on wikipedia.

AUTHOR

Will Coleda will@coleda.com

COPYRIGHT AND LICENSE

Copyright 2026 Will Coleda

This library is free software; you can redistribute it and/or modify it under the Artistic License 2.0.