Negafibonacci
From Wikipedia, the free encyclopedia
Numeral systems by culture | |
---|---|
Hindu-Arabic numerals | |
Western Arabic Eastern Arabic Khmer |
Indian family Brahmi Thai |
East Asian numerals | |
Chinese Japanese |
Korean |
Alphabetic numerals | |
Abjad Armenian Cyrillic Ge'ez |
Hebrew Ionian/Greek Sanskrit |
Other systems | |
Attic Etruscan Urnfield Roman |
Babylonian Egyptian Mayan |
List of numeral system topics | |
Positional systems by base | |
Decimal (10) | |
2, 4, 8, 16, 32, 64 | |
3, 9, 12, 24, 30, 36, 60, more… | |
In mathematics, negaFibonacci numbers are the numbers such that the nth negaFibonacci number is equal to the nth Fibonacci number multiplied by (-1)^n.
The first 10 negaFibonacci numbers are 1,-1,2,-3,5,-8,13,-21,34,-55.
Any integer can be represented as a unique sum of negaFibonacci numbers. For example -11 can be written as (-8) + (-3). This allow a coding of numbers, similar to the representation of Zeckendorf's theorem for coding numbers using a binary representation, where each binary digit represents the n'th negaFibonacci number.