I learn something new. But it is "Knuth". I Googled "Knut" and got
nothing mathematical and had to find it by "Wiki drilling".
3^^^3 is 3^3^3...^3 where "3" appears 7,625,597,484,987 times.
Unfortunately I am unable to calculate the number of digits in that
number as my Cray computer is currently being used by a bunch of hard
core gamers :-)
Is that "Conway of the knot"?
Mark
--- In [email protected], "prokofiev2006"
<alexis.monnerotdumaine@...> wrote:
nothing mathematical and had to find it by "Wiki drilling".
3^^^3 is 3^3^3...^3 where "3" appears 7,625,597,484,987 times.
Unfortunately I am unable to calculate the number of digits in that
number as my Cray computer is currently being used by a bunch of hard
core gamers :-)
Is that "Conway of the knot"?
Mark
--- In [email protected], "prokofiev2006"
<alexis.monnerotdumaine@...> wrote:
>in
> Talking about that, what do you think about this incredibly fast
> growing sequence ? :
> 0
> 1^1
> 2^^2
> 3^^^3
> 4^^^^4
> where "^" is not the usual power, but the arrow of Knut.
> The notation of Knut is defined this way:
> a^^^n = a^^(a^^(a^^�&a)) where a appears n times
>
> It then goes this way:
> 0 = 0
> 1^1 = 1
> 2^^2 = 2^2 = 4
> 3^^^3 = 3^^(3^^3) = 3^^X = 3^(3^(3^�&3)), where "3" appears 19683
> times, (because 3^^3 = 19683).
> A giant cookie for the one who can calculate how many figures are
> this number.indices -
>
> Alexis
>
> PS : For those who are not afraid about heights, I can show another
> even more nauseus sequence based on another notation : the notation
> of Conway.
> PS'': we are quite far from LT, here J
>
>
>
> --- In [email protected], "Mark" <secret.squirrel@> wrote:
> >
> > Yes, but you have to take care how you calculate compound
>so
> > unlike addition and multiplication, they are not associative;
> > ie (3^3)^3 = 27^3 = 19,683 but 3^(3^3) = 3^27 = 7,625,597,484,987.
> >
> > Mark
> >
> > --- In [email protected], "prokofiev2006"
> > <alexis.monnerotdumaine@> wrote:
> > >
> > > Very nice ! (or should I say "very nice !!")
> > > Simple and elegant sequence.
> > > And growing very fast.
> > > In the same idea, one can define : 0, 1^1, 2^2^2, 3^3^3^3 and
> on.
> > >
> > > Alexis
> > >
> > >
> > >
> > >
> > > --- In [email protected], "Mark" <secret.squirrel@>
> wrote:
> > > >
> > > > Zara is the Cookie Master!
> > > >
> > > > Very minor correction: 1st term is actually 0 (no factorial)
> > > >
> > > > Alexis and Suyono - you missed by one "!" !
> > > >
> > > > Mark
> > > >
> > > >
> > > > --- In [email protected], Juan Antonio Zaratiegui
> > > Vallecillo
> > > > <yozara@> wrote:
> > > > >
> > > > > Mark escribió:
> > > > > > Alexis, Suyono, Zara
> > > > > >
> > > > > > You are all very close!
> > > > > >
> > > > > > Zara - I agree with you. No nasty Excel stuff in my
> formula.
> > > The
> > > > most
> > > > > > advanced/complicated "function" is factorial.
> > > > > >
> > > > > > I'll let you all have a sniff of the cookie jar to
> encourage
> > > > you :-)
> > > > > > *opens lid*
> > > > > >
> > > > > > mmmm..mmmhhhh
> > > > > >
> > > > > > Mark
> > > > > >
> > > > > >
> > > > >
> > > > > These cookies smell really nice!
> > > > >
> > > > > First term is
> > > > > Second term is 1!
> > > > > Third term is 2!!
> > > > > Fourth term is 3!!!
> > > > > Fifth term is 4!!!!
> > > > > Sixth term is 5!!!!!
> > > > >
> > > > > nth term is (n-1)(!^(n-1)), so to say
> > > > >
> > > > > Zara
> > > > >
> > > >
> > >
> >
>