[seqfan] Re: The mysterious Layman sequences

[Peter Munn]

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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