zeck {numbers} | R Documentation |
Zeckendorf Representation
Description
Generates the Zeckendorf representation of an integer as a sum of Fibonacci numbers.
Usage
zeck(n)
Arguments
n |
integer. |
Details
According to Zeckendorfs theorem from 1972, each integer can be uniquely represented as a sum of Fibonacci numbers such that no two of these are consecutive in the Fibonacci sequence.
The computation is simply the greedy algorithm of finding the highest
Fibonacci number below n
, subtracting it and iterating.
Value
List with components fibs
the Fibonacci numbers that add sum up to
n
, and inds
their indices in the Fibonacci sequence.
Examples
zeck( 10) #=> 2 + 8 = 10
zeck( 100) #=> 3 + 8 + 89 = 100
zeck(1000) #=> 13 + 987 = 1000
[Package numbers version 0.8-5 Index]