Thread: Dodecaproths
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Old 2006-01-16, 11:54   #28
R. Gerbicz
 
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"Robert Gerbicz"
Oct 2005
Hungary

7·211 Posts
Default Estimation of the number of dodecaproths for n

As I estimated the number of octoproths for a given n value, it is also possible to give an estimation for dodecaproths:
Let's define the "weight" for n:
Code:
w(n)=T=2048.0;forprime(p=3,10^4,l=listcreate(12);g=Mod(2,p)^n;h=1/g;a=[g,-g,h,-h,2*g,-2*g,h/2,-h/2,4*g,-4*g,h/4,-h/4];\
a=lift(a);for(i=1,12,listput(l,a[i],i));l=listsort(l,1);T*=(1-length(l)/p)/(1-1/p)^12);return(T)
then by this we can estimate the number of dodecaproths for a given n by:
Code:
f(n)=round(w(n)*2^n/(n*log(2))^12*1/64)
For example if n=53 then f(n)=4. The true number is 6.
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