Hail suspect or Kakutani Theorem

(I) What is hail guess?

Hail guess means: a positive integer x, if it is an odd number multiplied by 1 plus 3, it is even if the even deposition factor 2ⁿ, so that after a number of times, and ultimately back to 1.

Regardless of how the value of this process huge, like a waterfall as quickly fall. Other figures if not so, after several transformation also bound to the even pure: the cycle 16-8-4-2-1.

According to research studies mathematician Japan and the United States, in all the positive integers less than 7 * 10 ^ 11, are in line with the law.

(Ii) write code in JavaScript

<! DOCTYPE HTML > 
< HTML lang = "EN" > 
< head > 
    < Meta charset = "UTF-. 8" > 
    < title > hail guess or angle ancient Theorem </ title > 
</ head > 
< body > 
< Script > 
    var X = the parseInt (prompt ( " enter a positive integer " ));
     the while (X != 1){
        if(x%2 == 0){
            X = X / 2; // if it is even precipitated the even factor 2ⁿ 
        }
         the else { 
            X = X * 3 + . 1 ; // if it is multiplied by an odd number plus 3. 1 
        } 
    document.write (X + " <br> " ); 
    } 
</ Script > 
</ body > 
</ HTML >

Example: Input Input 90☟ 9☟

(Iii) The powerful 27

⑴ 27 calculates according to the method described above, it is vigorously float sink exception: First, the step 27 to the converted 77 reaches its peak value 9232, and then through trough 34 reaches a step.

⑵ whole transformation process (referred to as "hail process") needs to step 111, which is the peak value of 9232 reached 342 times the original number of 27;

If ⑶ straight drop waterfall (N th power of 2) to compare the process with the same number N hail 111 to achieve a power of two.

⑷但是在1到100的范围内，像27这样的剧烈波动是没有的（54等27的2的次方倍数的数除外。）

如图所示：27的归一步数要经过多次剧烈波动的奇偶变换，其路径呈不光滑锯齿

Hail suspect or Kakutani Theorem

Guess you like