Typo in A074473
Lßbos ElemÚr
Labos at ana.sote.hu
Mon Sep 18 09:38:46 CEST 2006
On 15 Sep 2006, at 16:40, N. J. A. Sloane wrote:
> Jose Brox commented (correctly) that A074473 is somewhat unsatisfactory.
what it means "somewhat" ?
> I am changing the description and adding a new version A102419
> which will serve as a bridge with A060445.
>
> These changes won't be visible until the
> next update, which may not be for a few
> days - I am in the middle of a huge update,
> trying to get caught up with commenmts
> from the past two weeks
>
> NJAS
I guess I know what is one of your problem...:
in every iteration when speaking about a segment of an
iteration-list you can include or exclude the initial and/or
terminal (eg fixed point) entry. Just like in case of
variants of an interval (open, closed, semiclosed from
left or right...).
Consequently and formally length concepts can
be defined in 4 different manner.
This is a question of convention similar to Fahrenheit vs Celsius..
or Arabian vs Roman numbers like: I,II,III,IV,XIV,HIV,etc...
-----
Concerning the name using "...time" like terminology..
I do not care. However the 4 possible definitions with
any choice of name still remains independent.
And not specific to Collatz-iteration....
-------------
There is a vast,huge philosophical literature of
connection time with natural numbers including intuitionism
as well.
------------
For Collatz f(1)=1 has to be fixed.... Without this fixation
Wolfram Mathematica and other language programs do not work....
Concerning A074473(1) either 1 or arbitrary 0 is legitimate but
fixation of Collatz(1)=1 is desirable to avoid 1,4,2,1,4,2,1,...cycle.
------------
All the best
Labos
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