The Kitchen Sink and Other Oddities

Atabey Kaygun

Collatz Sequence in Binary

Description of the problem:

I like experimenting with the Collatz sequence. Today, I would like to display the binary representation of the Collatz sequence with a randomly selected initial point.

The code

The following function generates the sequence (only the odd part) from an initial seed.

(defun collatz (n &optional carry)
  (cond
    ((< n 1) nil)
    ((= n 1) (cons 1 carry))
    ((zerop (mod n 2)) (collatz (/ n 2) carry))
    ((collatz (1+ (* 3 n)) (cons n carry)))))

COLLATZ

And the following code snippet prints the binary representation:

(dolist (x (collatz (random (expt 2 50))))
    (format t "~50b~%" x))

NIL
                                                 1
                                               101
                                            110101
                                            100011
                                             10111
                                            111101
                                         101000101
                                         110110001
                                        1001000001
                                      110000000101
                                      100000000011
                                       10101010111
                                        1110001111
                                      100101111101
                                       11001010011
                                       10000110111
                                        1011001111
                                         111011111
                                         100111111
                                         110101001
                                         100011011
                                         101111001
                                          11111011
                                          10100111
                                         110111101
                                        1001010001
                                         110001011
                                         100000111
                                          10101111
                                          11101001
                                          10011011
                                           1100111
                                          10001001
                                           1011011
                                           1111001
                                          10100001
                                           1101011
                                           1000111
                                            101111
                                           1111101
                                           1010011
                                            110111
                                         100100101
                                        1100001101
                                   100000100010101
                                    10101101100011
                                    11100111011001
                                   100110100100001
                                110011011010110101
                               1000100100011110001
                                101101101101001011
                               1111001111000011101
                               1010001010000010011
                                110110001010110111
                                100100000111001111
                                110000001001101001
                                100000000110011011
                                 10101011001100111
                                 11100100010001001
                                 10011000001011011
                                  1100101011100111
                                 10000111010001001
                                  1011010001011011
                                  1111000001111001
                                 10100000010100001
                                 11010101110000001
                                100011101000000001
                                101111100000000001
                                 11111101010101011
                                 10101000111000111
                                  1110000100101111
                                  1001011000011111
                                  1100100000101001
                                 10000101011100001
                                  1011000111101011
                              11101101001110010101
                            1001111000100110001101
                             110100101101110110011
                         1000110010010011101110101
                          101110110110111110100011
                           11111001111010100010111
                           10100110100111000001111
                            1101111000100101011111
                            1001010000011000111111
                            1100010101110110101001
                            1000001110100100011011
                            1010111110000101111001
                             111010100000011111011
                             100111000000010100111
                            1101000000000110111101
                            1000101010101111010011
                             101110001110100110111
                              11110110100011001111
                              10100100010111011111
                               1101101100100111111
                              10010010000110101001
                              11000010110011100001
                              10000001110111101011
                               1010110100101000111
                               1110011011100001001
                               1001100111101011011
                                110011010011100111
                               1000100011010001001
                               1011011001101100001
                                111100110011101011
                               1010001000100111001
                             110110000011010000101
                            1001000000100010110001
                           11000000001011100101101
                           10000000000111101110011
                            1010101011010011110111
                          111000111100010100100101
                        10010111110110001100001101
                       110010100111011001011001101
                      1000011011111001100100010001
                      1011001111110111011011000001
                    111011111111010010010000000101
                    100111111111100001100000000011
                     11010101010010110010101010111
                 100011100011001000011100011110101
                 101111011001100000100101111110001
          1111110011001010110111010100101101010101
         10101000100001110011111000110010001110001
       1110000010110100010100101110110110100000101
      10010101110011011000110010011110011010110001
      11000111101111001011101101111101111001000001
   10000101001010000111110011111110100110000000101
   10110001100010110101000101010011011101010110001
   11101100101110011100000111000100100111001000001
 1001110111010001001010111101100001101000010101101
  110100100110110000111010011101011110000001110011
 1000110001001000001001101111100101000000010011001
 1011101100001010110111101010000110101011000100001
  111110010110001111010011100000100011100101101011
 1010011001000010100011010000000101111011100111001
  110111011010111000010001010101110100111101111011

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