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I did a study of the Collatz conjecture and came to the conclusion that all even numbers can be removed from the Collatz conjecture because even numbers act as the connecting links between odd numbers. What do you think about it? Is it a breakthrough in 3n+1 problem?
To get the number 27, we just need to start from 1 and use three rules, (2n-1)/3, (4n-1)/3 and 4x+1.
1 -> 5 -> 3 -> 13 -> 53 -> 35 -> 23 -> 15 -> 61 -> 81 -> 325 -> 433 -> 577 -> 769 -> 3077 -> 2051 -> 1367 -> 911 -> 607 -> 2429 -> 1619 -> 1079 -> 719 -> 479 -> 319 -> 425 -> 283 -> 377 -> 251 -> 167 -> 111 -> 445 -> 593 -> 395 -> 263 -> 175 -> 233 -> 155 -> 103 -> 137 -> 91 -> 121 -> 161 -> 107 -> 71 -> 47 -> 31 -> 41 -> 27.
To get the number 27, we just need to start from 1 and use three rules, (2n-1)/3, (4n-1)/3 and 4x+1.
1 -> 5 -> 3 -> 13 -> 53 -> 35 -> 23 -> 15 -> 61 -> 81 -> 325 -> 433 -> 577 -> 769 -> 3077 -> 2051 -> 1367 -> 911 -> 607 -> 2429 -> 1619 -> 1079 -> 719 -> 479 -> 319 -> 425 -> 283 -> 377 -> 251 -> 167 -> 111 -> 445 -> 593 -> 395 -> 263 -> 175 -> 233 -> 155 -> 103 -> 137 -> 91 -> 121 -> 161 -> 107 -> 71 -> 47 -> 31 -> 41 -> 27.
