Re: factorial sequence proposal

"I.N. Galidakis" :
wugi wrote:

The basic idea is, implementing factorials of factorials, or "powered"
factorials.
So I came to use the notation !, !!, !!!, .... !^k, although I found
out that !! is being used for less exciting (in my view) definitions.

A sequence needs a starting number, or seed n : hence,
Seq = Seq(n), with terms a(k)=Seq(n,k) as follows:
a(0) = n
a(1) = n!
a(2) = a(1)! = (n!)! == n!!
.....
a(k) = a(k-1)! = n(!!...!!) == n(!^k)

The idea is not really new. People have worked with iterated factorials
before.

For example:

http://ioannis.virtualcomposer2000.com/math/hfseries.html

There is a reference given to me by Dave L. Renfro in AMM Problems (which
I
can't find right now) which gives bounds for it. Using your notation (and
if
memory serves right):

n^^k < n(!^k) < n^^(k+1),

where ^^ is the tetration operator. Perhaps that's why your sequence
didn't make
it to OEIS.

Thank you.
But didn't OEIS aspire comprehensiveness? So if one signals not having found
such or so a series in their site, one likes at least to be pointed to it,
or any other reply. The application procedure also does (apparently) only
take specific number examples; parametered formulas seem out of question,
ruling out god knows how many cases.
A by-observation for the series above:
2 is apparently a unit seed (besides 1), as we get
2=2!=2!!=2!!!=....

guido
http://home.scarlet.be/~pin12499


.