[seqfan] Re: A054353 and A099467

[jean-paul allouche]

Dear Андрей

Many thanks for your convincing explanations
best wishes
jp

Le 10/02/2021 à 22:23, Андрей Заболотский via SeqFan a écrit :
> 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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