[seqfan] Re: Message from Marc LeBrun

Jeffrey Shallit shallit at uwaterloo.ca
Thu May 12 11:46:51 CEST 2016




>> ...the Beatty sequence
>>     floor(n*alpha) for n >= 1
>> is an eigensequence for the discriminator if and only if
>> 1 <= alpha < 3/2.  There is a one-line proof!
>
>    Thanks, Dr. Shallit.
>    It's more than just Beatty sequences. If a sequence begins "1,2",
>    and thereafter (a(n+1) - a(n)) is in {1,2}, it's an eigensequence.
>

Yes, this is my one-line proof.


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