Kata

Description

Do you know Collatz conjecture? Click here, You can read some details..

Given the following algorithm (Collatz conjecture):

  If number x is even, x = x / 2
  else if x is odd, x = x * 3 + 1

Find all the possible numbers(x) which resolve to a specified number (y) when the algorithm is applied a specified number of times (n).

Sort the results in ascending order.

For example:

Find all the possible numbers which resolve to 1 (y = 1) after 5 applications of the algorithm (n = 5). (in accordance with the rules of the Collatz conjecture)

reversalCollatz(5,1) === [4,5,32]

Because:
4  -> 2  -> 1 -> 4 -> 2 -> 1

5  -> 16 -> 8 -> 4 -> 2 -> 1

32 -> 16 -> 8 -> 4 -> 2 -> 1

More Examples

reversalCollatz(5,1) === [4,5,32]

reversalCollatz(3,12) === [48]

reversalCollatz(4,7) === [9,56]