[seqfan] Re: Fractal sequence A087088
Kevin Ryde
user42_kevin at yahoo.com.au
Wed Jul 15 12:22:25 CEST 2020
acwacw at gmail.com (Allan Wechsler) writes:
>
> something like "Positive ruler-type
> fractal sequence with 1's in every third position."
Concerning rulers, I've mentioned elsewhere I struck this sequence as
"how far carry propagates when incrementing in base 3/2", which is
ruler-like.
However my base 3/2 is an unusual variant with digits -1/2, 0, +1/2
except highest digit 1, and "integer prefixing" (still integer if
discard least significant digit). I haven't encountered this elsewhere
and don't know whether the concept is good beyond my own use so-far.
A more straightforward, and more or less equivalent, interpretation is
how far up to the common ancestor of n and n+1 in a certain tree defined
by 2 children for odd and 1 child for even -- counting positions across
each tree row. Here's a rough picture.
http://user42.tuxfamily.org/temporary/A087088-tree.pdf
I'll have to try a bigger better picture for something visual.
The descents follow without much trouble from the recurrence formulas,
or Benoit Cloitre's construction.
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