[seqfan] Re: The mysterious Layman sequences

[Peter Munn]

I meant "1 - 1/phi", equivalently "phi^-2", not "1 - phi".

Peter

On Fri, May 14, 2021 1:56 am, Peter Munn wrote:
> Doug's "wild guess" below seems very reasonable, as in a simpler case, it
> looks easily provable that the Fibonacci bisection, A001906, will be
> generated by any c satisfying 1 - phi < c <= 0.5, where phi is the golden
> ratio.
>
> Best regards,
>
> Peter
>
> On Fri, May 14, 2021 12:25 am, D. S. McNeil wrote:
>> I'm getting similar results, but I'm also finding the same behaviour
>> with
>> c
>> = 0.37-- the first 20k values appear to be the same.
>>
>> Looking at a plot of the x/y ratios observed during the calculation,
>> there
>> do seem to be excluded bands -- regions where no such ratio is ever
>> observed.
>>
>> So (wild guess time) maybe there's nothing special about the magic
>> number
>> 0.36704.  It's part of a band of numbers that generate the same first
>> few
>> elements of the sequence and then puts them on a path where ratios
>> nearby
>> the threshold aren't observed, meaning the sequences won't diverge
>> despite
>> their apparently different definitions.
>>
>>
>> Doug
>>
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>>
>
>
>
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>