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Title: Collatz conjecture or 3x+1 problem Post by: iamrohitkgupta on November 22, 2016, 05:13:54 PM Quote Conjecture: Take any positive integer x. If x is even, divide it by 2(x/2). Else n is odd, multiply it by 3 and add 1(3*x+1). The conjecture is that no matter what number you start with, you will always eventually reach 1. Eg: 10 is even 10/2 = 5 is odd 5*3+1 = 16 is even 16/2 = 8 is even 8/2 = 4 is even 4/2 = 2 is even 2/2 = 1 is odd 1*3+1 = 4 and the cycle continues. I was Playing with Python and this problem. I calculated the number up-to 10,485,760 which takes maximum steps to get to 1 : Maximum Counts: 685(+/-1) Even Counts: 429 Odd Counts: 256 Number with maximum Counts: 8400511 Not sure if this is correct. Some time later I thought about trying negative numbers and I noticed 3 patterns: pattern 0: -2 -1 pattern 1: -14 -7 -20 -10 -5 pattern 2: -50 -25 -74 -37 -110 -55 -164 -82 -41 -122 -61 -182 -91 -272 -136 -68 -34 -17 Numbers from -1 to -16 either follow pattern 0 or pattern 1, but -17 on wards some of them follow pattern 2. There might be other patterns too, but I haven't come across any, yet. Has anyone (other than me) tried it? Title: Re: Collatz conjecture or 3x+1 problem Post by: arara on November 22, 2016, 05:18:54 PM could not understand the problem ???
Title: Re: Collatz conjecture or 3x+1 problem Post by: iamrohitkgupta on November 22, 2016, 05:29:41 PM could not understand the problem ??? Forgive me, I forgot to state the conjecture:Take any positive integer x. If x is even, divide it by 2(x/2). Else n is odd, multiply it by 3 and add 1(3*x+1). The conjecture is that no matter what number you start with, you will always eventually reach 1. Also updated the Original Post. |