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.