Triple FJS

[Joerg Arndt]

I guess my answer was (too-) quick shot.
The constructions seemed similar to me but
I could (later) not find anything useful.
Still one may want to check whether your sequences
are fixed points of some morphism.

I played with sequences of the "fixed point of a morphism"-type
a while ago and was surprised how closely many of the
better known 2-automatic sequences are related.

There is a (very experimental, un-mathematical) section
("synthetic iterations", the very last section)
in teh draft text http://www.jjj.de/fxt/#fxtbook .
Note that the emphasis there is the computation of functions
that are generalizations of these sequences.

* Eric Angelini <keynews.tv at skynet.be> [May 03. 2005 15:44]:
> 
> Hello Hugo and Joerg,
> 
> [Hugo ]:
> 
> > It reminds me of a sequence discussed by Hofstadter [0],
> > of the number of triangular numbers between each successive
> > pair of squares. I'm not sure, but I think this is A006338
> > (...)
> 
> ... The two sequences differ: (DH stands for D.Hofstadter and
> FJ for Fractal Jump):
> 
> DH. : 21211212121 1 2121121212 1 121 2 1 12 1 2 1 1 2 ...
> FJ. : 21211212121 2 2121121212 2 121 1 2 12 2 1 2 1 1 ...
>                   ^            ^     ^ ^    ^ ^ ^   ^ 
> -----------
> 
> [Joerg]:
> 
> > You might want to check A035263 "period-doubling sequence"
> 
> ... I did but... couldn't see the link -- is there a relation-
> ship? If I turn the 1's and 0's of A035263 into 1's and 2's 
> of the above FJ (or 2's and 1's), I see no match :-(
> 
> 
> FJ. : 21211212121221211212122121121221211 ...
> A035. 10111010101110111011101010111010101 ...
> 0>2   12111212121112111211121212111212121 ...
> >2+1  21222121212221222122212121222121212 ...
> FJ. : 21211212121221211212122121121221211 ...
>         ^^^^^^^^^    ^^^^ ^^    ^ ^^    ^
> 
> Best to both of you,
> E.
> 
-- 
p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0
Life is hard and then you die.