Re: [math-fun] Collatz 3N+1 problems

Just for fun, tried a new algorithm in this vein recently, a mapping f: Odds+ -> Odds+ defined by: first doing N -> M=(3N+1)/2^K (where 2^K | 3N+1, but 2^(K+1) doesn't) and then doing M -> P=(3M-1)/2^L (where 2^L | 3M-1, but 2^(L+1) doesn't) We then say P = f(N). Trying each odd from 1 to 10,000, found the trivial cycle, a fixed point of f: C_1: 1 (-> 1) and the lone interesting cycle C_17: 17 -> 19 -> 43 -> 97 -> 109 -> 61 (-> 17). An interesting question (IF all positive integers fall into one or the other of these cycles) is: What fraction of pos. ints. fall into C_1, and what fraction fall into C_17 (assuming these sets have densities). --Dan