Talk:Zeckendorf number representation: Difference between revisions
Talk:Zeckendorf number representation (view source)
Revision as of 00:32, 12 October 2012
, 11 years ago→Consensus on the sequence: tea leaves
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: The sequence should be specified as 1,2,3,5,8..., and a Zeckendorf representation of a non-negative integer n is n expressed as the sum of non-consecutive terms in that sequence. This is sufficient and unambiguous: every n >= 0 has a unique such representation, and vice versa. I don't think the task should specify ''how'' one derives such a summation from n; listing a method as a hint, fine, putting it in the spec as if it's required, no. --[[User:Ledrug|Ledrug]] 23:47, 11 October 2012 (UTC)
:: I agree with these points. I'll add that it seems most sites say Zeckendorf representation only specifies a sum, and does not specify the binary place value coding that turns 3 + 1 into 101. I kind of like the binary coding but I think it might be good to describe it as an additional encoding on top of Zeckendorf representation. [http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibrep.html#fibbase Dr Ron Knott's site] calls this the "Fibonacci base system." Other links:
::* [http://mathworld.wolfram.com/ZeckendorfRepresentation.html Mathworld] hints at the binary encoding by using 0 or 1 as a multiplier of Fibonacci terms.
::* [http://mathworld.wolfram.com/ZeckendorfsTheorem.html Z's theorem at MathWorld]
::* [http://en.wikipedia.org/wiki/Zeckendorf%27s_theorem Wikipedia] is careful to say the theorem applies to ''distinct'' Fibonacci numbers (my emphasis.)
::* [http://oeis.org/A003714 OEIS A003714], "Fibbinary numbers".
:: —[[User:Sonia|Sonia]] 00:32, 12 October 2012 (UTC)
==Perl 6, wrong fib sequence==
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