fractal sequences

Meeussen Wouter (bkarnd) wouter.meeussen at
Mon May 26 16:25:57 CEST 2003

thanks to Superseeker,
my nose was pressed on the fact that A066194 = 1 + A003188(Gray code).

Blush, blush

how could I have known, apart from recognising it 'on sight'?


-----Original Message-----
From: Ralf Stephan [mailto:ralf at]
Sent: maandag 26 mei 2003 11:49
To: Seqfan (E-mail)
Subject: Re: fractal sequences

> example: A066194 :: plot it as (x= k, y= a[k])
> (??)
> How many are at the same time a permutation over (all) the integers like
> A066194?

There is the evergreen A003188 (Gray code). It is 2-regular, which
I conjecture herewith A066194 to be, too. And I'll add, again, that
I suspect any self-similar sequence to have that property, as well as
having an ogf that is expressible as an infinite sum where k is in
the exponent of x. Most 2-regulars have an ogf with sum...x^2^k..., 
for example.

Can you prove it?


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