MUCH BETTER!

In fact it’s better in two ways – closer still to “parity,” AND a better fit with “evil” and “odious”! Gets my vote right off. JHC

]]>“Upon the bed, before the whole company, there lay a nearly liquid mass of loathsome——of detestable putrescence.”

The distastefulness of the subject notwithstanding, don’t you find “putrescence” a much more lilting word than “putridity”?

🙂

]]>the “classic” Thue-Morse seq. can be expressed as a(n)=S2(n)mod 2, where S2(n) = sum of digits of n, n in base-2 notation. A year ago I was looking on the more general case :

Let Sk(n) = sum of digits of n; n in base-k notation. Let F(t) be some arithmetic function.

Then a(n)= F(Sk(n)) mod m is a generalised Thue-Morse sequence.

Nice properties have sequences where F(Sk(n))=floor(Q*Sk(n)); Q is a positive rational number.

Partial sums of a generalized Thue-Morse sequence a(n)=F(Sk(n)) mod m are fractal –> they consist of series of the generalized batrachion Blancmange function (similarly to Hofstadter’s Q-Sequence, Hofstadter-Conway 10000$ and Mallows seq. etc.). A good article is https://arxiv.org/PS_cache/math/pdf/0406/0406078v1.pdf which mirrors my computational results from an ergodic/Pascal-adic transformation point of view. Partial sums of such generalized Thue-Morse seq. also points to the Minkowski Question Mark function and relates the continued-fraction representation of the real numbers to their k-ary expansion https://arxiv.org/PS_cache/arxiv/pdf/0810/0810.1265v2.pdf.

I do not know if my note is of interest for you,

Have a nice day,

Ctibor

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