11/03/2010, 05:26 AM

(10/18/2010, 12:09 AM)nuninho1980 Wrote:Pentation is hard to understand.... Here's my results. I used "b" for the base.

By the results have 5 cases decimais (minimum).

Please you think to calculate on up... I have known its by program Pari/GP (it's very fast). x)

, for each "n", calculate b

, calculate b

, calculate b

, calculate b

and so on, limit as

n= 2 1.63221539635499

n= 3 1.73480823757765

n= 4 1.73013167405422

n= 5 1.71198477313212

n= 6 1.69588829898111

n=70 1.63599652477221

I calculated these values by simple binary search, but I used "\p 28", which is accurate to ~14 digits, but very fast, 4 seconds for init(B);loop. Only problem is its very easy to get an overflow, so the initial starting based needs to readjusted; for n=70, I used a more complicated algorithm.

Code:

`\r kneser.gp`

\p 28;

{ curbase=1.6;

curstep=0.1;

while ((curstep>1E-14),

init(curbase);loop;

y = sexp(sexp(B));

if (y>3, curbase=curbase-curstep, curbase=curbase+curstep);

curstep=curstep/2;

); }

As n goes to infinity, I would expect the value for b to go to Nuinho's constant, the base for which the upper fixed point of sexp is parabolic,

b=1.635324496715276399345344618306171

- Sheldon