Collatz Revisted ------- -------- Consider the operation F(N) defined as: F(N) = N/2 if N can be divided by 2 F(N) = N/3 if N can be divided by 3 F(N) = 5N + 1 otherwise We conjecture that for any natural number N, applying F repeatedly to any non-zero natural number will eventually arrive at the number 1. Thus [1] F(5) = 26 [2] F(26) = 13 [3] F(13) = 66 [4] F(66) = 33 [5] F(33) = 11 [6] F(11) = 56 [7] F(56) = 28 [8] F(28) = 14 [9] F(14) = 7 [10] F(7) = 36 [11] F(36) = 18 [12] F(18) = 9 [13] F(9) = 3 [14] F(3) = 1 so F applied 14 times starting at 5 will get to 1. The original Collatz Conjecture, named after Lothar Collatz, who first proposed it in 1937, is for a simpler F, and has never been proved or disproved. Given N, you are to find the number of times F must be applied starting at N to get to 1. Input ----- Input contains several test cases. For each test case there is one input line containing N. Input ends with an end of file. All numbers N input will be such that applying F many times to N will not generate a number above 10^9. Output ------ For each test case, one line containing first N and then the number of times F must be applied starting at N to get to 1. Sample Input ------ ----- 1 2 3 4 5 6 7 8 9 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 Sample Output ------- ------ 1 0 2 1 3 1 4 2 5 14 6 2 7 5 8 3 9 2 10 15 100 11 1000 28 10000 28 100000 55 1000000 44 10000000 90 100000000 55 1000000000 87 File: collatz2.txt Authors: Tom Widland Bob Walton Date: Tue Oct 8 07:49:59 EDT 2019 The authors have placed this file in the public domain; they make no warranty and accept no liability for this file.