[seqfan] Re: A054353 and A099467

[Андрей Заболотский]

Interesting. However, in the 2nd thousand of terms there’s only one coincidence.
An observation about A099467 (must be easy to prove):
it seems that the first differences are 1 and 2 strictly alternately, except near powers of 2: a(2^k+2)-a(2^k+1) = a(2^k+1)-a(2^k).
This explains why the sequences are close to each other: both have 1st differences consisting of 1’s and 2’s in equal proportion, mixed very well.
 
Best regards,
Andrey Zabolotskiy
  
>Среда, 10 февраля 2021, 23:46 +03:00 от jean-paul allouche <jean-paul.allouche at imj-prg.fr>:
> 
>Dear all
>
>Comparing A054353 (partial sums of Kolakoski) and A099467 seems
>to show some sort of "similarity": many terms coincide and the other
>terms seem close to their counterpart. I do not see any reason why it
>is so (actually this is seen on the first displayed terms). Any hint?
>
>thank you
>best
>jp
>
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