abc conjecture - abc streams (sequences of creek stones)

A sequence of natural numbers $\ (c_n: n=1\ 2\ \ldots)\ $ is called a sequence of creek stones $\ \Leftarrow:\Rightarrow\ \forall_{n=1\ 2\ \ldots}\,c_{n+1}\ge c_n^2\ $.Given natural $\ a\ b,\ $ such that $\ \gcd(a\ b) = 1,\ $ define $\ S(a\ b)\ :=\ \frac{L(a\ b)-1}{L(a\ b)+1},\ $ where$$\ L(a\ b) := \frac{\log(c)}{\log(rad(a\cdot b\cdot(a+c)))} $$is the Browkin-Brzeziński flavor of the abc coefficient.A sequence of natural triples $\ ((a_n\ b_n\ c_n):n=1\ 2\ \ldots)\ $ is called an abc stream $\ \Leftarrow:\Rightarrow\ \forall_{n=1\ 2\ \ldots}...Read more