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(k1,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 k1 of
x(i,n)*((3^(x(i+1),n)+...+x(k1,n))/2^(ki)
?
