[seqfan] Re: The discriminator of a sequence

Don Reble djr at nk.ca
Wed May 4 13:25:42 CEST 2016


Seqfans:

> take a sequence a(n) and compute its discriminator and you get a new
> sequence!

    ...unless a(n) has repeated values.

> It would be interesting to see what happens when this is applied to
> all our favorite sequences.

    Usually you get a new sequence, but the OEIS may have a few old
    discriminators. I haven't proven anything, just computed as far
    as the %STU lines go.

    D(A000027) -> A000027 (obviously)
    D(A000062) -> A000062 (eigensequence)
    D(A000069) -> A062383
    D(A000124) -> A062383
    D(A000217) -> A062383
    D(A000384) -> A062383
    D(A000447) -> A062383
    D(A001068) -> A047201
    D(A001109) -> A062383
    D(A001477) -> A000027 (obviously)
    D(A001637) -> A000027
    D(A001651) -> A001651 (eigensequence)
    D(A001824) -> A062383
    D(A001955) -> A001955 (eigensequence)
    D(A001961) -> A001961 (eigensequence)
    D(A002180) -> A002180 (eigensequence)
    D(A002473) -> A002473 (eigensequence)

    It seems that Beatty sequences (A62, A1955, A1961) are often
    eigensequences; many discriminators have just powers of two (A62383).

-- 
Don Reble  djr at nk.ca



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