Typo in A074473

[Lßbos ElemÚr]

On 11 Sep 2006, at 19:59, Tautócrona wrote:

> 
> Hi all!
> 
> I've got a couple of comments to seq A074473 that supposedly is
> 
> "Number of iteration that first becomes smaller than the initial value if Collatz-function
> (A006370) is iterated; a(1)=0 since no decrease is possible during iteration.
> 0, 2, 7, 2, 4, 2, 12, 2, 4, 2...
> "
> 
> First of all, in the literature this function is called the "stopping time function"
> (look, for example,
> http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/node2.html ), maybe we could
> add this name to its description.
> 
> Second, strangely the author considers that the first value of the trajectory of n, i.e.,
> n itself, is actually _the first iteration_ of the Collatz-function. I don't agree with
> this; as far as I know, n is usually considerated the zeroth iteration, and g^k(n) the
> k-th one, if g(n) is the Collatz function (so that g^0(n) = id(n) ). Then, all the numbers
> in the sequence have an undesired offset of 1 unit, except the first one, because the
> first iteration is that produced by g(n), and not by g^0(n).
> 
> I think we should change it... I near contributed the same sequence! (substracting one, of
> course!).
> 
> Regards. Jose Brox
> http://espanol.groups.yahoo.com/group/Telecomunicacion/
> ambroxius at terra.es
> MSN Messenger: artifex_ad_infinitum2 at hotmail.com
> 
Concerning initial value=1, you have to decide about
Collatz-iteration.
Leaving original you get 1,4,2,1,4,2,1, ... It means  no fixed point
but a cycle of 3 entries.
However if arbitrarily for iv = 1 you define Collatz[1]=1, then                
no ambiguity arising from definition. 
------------------
Concerning number of iterations or number of entries during 
iteration obviously differs by one. 
My definition is given by the program.. and self-explained also
by example. 
This is not a serious problem. It occurs in every iteration.
------------------
Concerning stopping time as a name: Please give a comment 
telling this quantity in 	question is called by this name in the 
literature... 
But give the guy who first used this terminus . You can provide also 
ten new names with suitable support.
-----------------
I did not give name I gave definition.
---------------
However.....
Although using term "time" is OK and no objection is necessary 
against,  but it is obviously a physical-tradition-association reflex. 
Philosophically it requires
a very abstract time in which all iterational step takes place
[or computed...] in equal physical time.
I accept time as a name but I can speak against:  it is not a 
computational time surely. It is not a physical time surely..
It is a natural number, nothing else but a result of a counting-
operation surely.
This iteration as a temporal happening is not a Collatz-iteration-
specific problem. 

Stop-time as a name is a tradition. Drop time is another tradition 
newly introduced by one of you. Cynically speaking,I would prefer:  
"time of expectation until my desire is satisfied, the  Collatz-
sequence started to decrease"....
In your place I would place the name problem into a 
comment...together with refererence... for "stop-time". 

All the best

Labos