[seqfan] Re: The Fibonacci word over the nonneg integers

hv at crypt.org hv at crypt.org
Sat Jul 1 09:34:11 CEST 2017

```Neil, in A104324 examples you have:
This sequence may be broken up into blocks of lengths 0,1,1,2,3,5,8,...
(the Fibonacci numbers). The first few blocks are:

0,
1,
2,2,
3,2,3,
4,2,3,4,4,
5,2,3,4,4,5,4,5,
[...]

.. which isn't the breaking up I'd have expected. I instead expected
something like:
Breaking up the sequence into the groups added by each iteration of
the morphism, after the initial zero, gives blocks of lengths
1,1,2,3,5,8 (the Fibonacci numbers). The first few blocks are:

1,
2,
2,3,
2,3,4
2,3,4,4,5,
2,3,4,4,5,4,5,5,
etc.

I'm not sure whether there's some different reading of the blocks you've
shown that motivates that grouping, so I haven't edited it.

Hugo

Neil Sloane <njasloane at gmail.com> wrote:
:Interesting new paper in the Electronic J Combinatorics:
:
:Jiemeng Zhang, Zhixiong Wen, Wen Wu, Some Properties of the Fibonacci
:Sequence on an Infinite Alphabet, Electronic Journal of Combinatorics,
:24(2) (2017), #P2.52.
:
:http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i2p52/pdf
:
:Trajectory of 0 under the map x -> x,x+1 if x is even, x -> x+1 if x is
:odd, starting at 0:
:
:0, 1, 2, 2, 3, 2, 3, 4, 2, 3, 4, 4, 5, 2, 3, ...
:
:The sequence was in the OEIS already but with a different definition:
:A104324
:
:It has many interesting properties.
:
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```