Talk:Zeckendorf number representation: Difference between revisions
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Mathworld's page on Zeckendorf's theorem mentions that it applies to {F-1}, that is, the Fibonacci sequence with one of the 1s removed, and presumably without the 0. —[[User:Sonia|Sonia]] 22:39, 10 October 2012 (UTC) |
Mathworld's page on Zeckendorf's theorem mentions that it applies to {F-1}, that is, the Fibonacci sequence with one of the 1s removed, and presumably without the 0. —[[User:Sonia|Sonia]] 22:39, 10 October 2012 (UTC) |
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: There simply can't be two 1s, otherwise a lot of numbers won't have unique summation: anything in for form of big_fib + 3 can also be written as big_fib + 2 + 1 (that's using the first one; the second one would be next to 2, if that makes sense -- well if it doesn't, it sort of proves the point also.) --[[User:Ledrug|Ledrug]] 01:27, 11 October 2012 (UTC) |
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Revision as of 01:27, 11 October 2012
Consensus on the sequence
Googling around, there seems to be a lack of consensus on the sequence of Fibonacci numbers used and how the sequence is indexed. If you include both F(1) = 1 and F(2) = 1, then the representation 1 is not unique. Similarly, if you include F(0) = 0, then the representation of 0 is not unique.
Mathworld's page on Zeckendorf's theorem mentions that it applies to {F-1}, that is, the Fibonacci sequence with one of the 1s removed, and presumably without the 0. —Sonia 22:39, 10 October 2012 (UTC)
- There simply can't be two 1s, otherwise a lot of numbers won't have unique summation: anything in for form of big_fib + 3 can also be written as big_fib + 2 + 1 (that's using the first one; the second one would be next to 2, if that makes sense -- well if it doesn't, it sort of proves the point also.) --Ledrug 01:27, 11 October 2012 (UTC)