numbers in numbers - divide by 2 - cyclic -algorithm compare

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We got cyclic of integers divide by 2 in number 2**n. Example:

                                                                        8192 is even number
                                                4096 is even number     4096 is even number
                        2048 is even number     2048 is even number     2048 is even number
    1024 is even number 1024 is even number     1024 is even number     1024 is even number
    512 is even number  512 is even number      512 is even number      512 is even number
    256 is even number  256 is even number      256 is even number      256 is even number
    128 is even number  128 is even number      128 is even number      128 is even number
    64 is even number   64 is even number       64 is even number       64 is even number
    32 is even number   32 is even number       32 is even number       32 is even number
    16 is even number   16 is even number       16 is even number       16 is even number
    8 is even number    8 is even number        8 is even number        8 is even number
    4 is even number    4 is even number        4 is even number        4 is even
   2 is even number     2 is even number        2 is even number        2 is even number
   1 is odd number      1 is odd number         1 is odd number         1 is odd number

second example number:

**8186 is even number       40930 is even number
4093 is odd number      20465 is odd number
4092 is even number     20464 is even number
2046 is even number     10232 is even number
1023 is odd number      5116 is even number
1022 is even number     2558 is even number
511 is odd number       1279 is odd number
510 is even number      1278 is even number
255 is odd number       639 is odd number
254 is even number      638 is even number
127 is odd number       319 is odd number
126 is even number      318 is even number
63 is odd number        159 is odd number
62 is even number       158 is even number
31 is odd number        79 is odd number
30 is even number       78 is even number
15 is odd number        39 is odd number
14 is even number       38 is even number
7 is odd number         19 is odd number
6 is even number        18 is even number
3 is odd number         9 is odd number
2 is even number        8 is even number**
1 is odd number         4 is even number
                        2 is even number
                        1 is odd number

how to analyze ciclic of divide number ? or how many ciclic are ?I mean I wuold like to perfom algorithm which will be detect probality divide number without knowing the number. it is cripto task.
for example we know that Point(X,Y) can be odd like 1,3,5,7,9 or even like 2,4,6,8, depends is odd we must substract 1 to get even, but if even we can divide 2. it must be analyze possibilities.