[seqfan] Re: Message from Marc LeBrun

Don Reble djr at nk.ca
Wed May 11 01:52:12 CEST 2016


> ...it would be interesting to see what the "greatest-confuser
> sequences" are like.

    The greatest confuser is the largest value minus the smallest.

> The sequence Bn of sets encoded 1-to-1 by the integers from 0 begins
>    {} {0} {1} {0 1} {2} {0 2} {1 2} {0 1 2} {3} {0 3} {1 3} {0 1 3} ...
> And (barring misteaks) the sequence of greatest confusers (ditto, arguably)
>    0 0 0 1 0 2 1 1 0 3 2 3 ... Not in OEIS?

    No, it's 0 0 0 1 0 2 1 *2* 0 3 2 3 ...  <also, "mistakes" >:->
    That is, 0,0,A119387.


    Regarding other messages,

> and for 2^n -1  or  2^n+1  is 1, 3, 5, 9, 11, 13, 19, 25,...
> for 3^n-1 or 3^n+1 1, 4, 5, 7, 17, 19, 25, 29, 31, 43,...

    Adding a constant throughout a sequence doesn't change the
    discriminators (nor the confusers).

> ...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.

    Hey! the lexically last discriminator eigensequence is already in OEIS.
    (Spoiler: the A-number is in both A032457 and A058842, but is not 63.)

-- 
Don Reble  djr at nk.ca



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