Typo in A074473

[T. D. Noe]

At 8:02 PM +0200 9/11/06, 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!).


Alternatively, we could just change the name and add another sequence that
counts the iterations.

A060445 gives the "dropping time" of odd numbers.  Although the term
"stopping time" is used in the literature, I think "dropping time" is more
descriptive.  Other terms are also used in the vast 3x+1 literature.

Tony