2020-07-02, 09:29 | #1 |
Mar 2018
2^{2}×7×19 Posts |
collatz 3x+1
I found a forumula about the 3x+1 problem
let be T(k,n) the trajectory starting from integer n. k is the number of iterations T(0,n)=n i think T(k,n)=n*lambda(k,n)+rho(k,n) how to proof that? where lamba(k,n)=(3^(x(0,n)+...+x(k-1,n))/2^k x(0,n)...is the parity vector of 1's and 0's, 1 if x(i,n) is odd and 0 if it is even rho is a sum from i=0 to k-1 of x(i,n)*((3^(x(i+1),n)+...+x(k-1,n))/2^(k-i) ? |
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