Typo in A074473

[Tautócrona]

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
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