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 in
this number.
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
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 in
this number.
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 indices -
> 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 so
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
> > > >
> > >
> >
>