Collatz conjecture
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| {{rowIndex}} | |
| Collatz sequence | {{value}} |
|---|---|
| Collatz sequence odd values | {{value}} |
"Collatz conjecture" conjecture
For any positive integer m, there are 3 values n1, n2 and n3, such that a Collatz sequence for n1, n2 or n3 will start with m consecutive continuously increasing odd values.
Stated in a different way: a Collatz sequence for n1, n2 or n3 will start with m consecutive odd values that are separated by one and only one even value between them.
Or, stated in yet another different way: a Collatz sequence for n1, n2 or n3 will start with 2m consecutive alternating odd and even values.
Those n1, n2 and n3 values are:
| If m is even | If m is odd | |
|---|---|---|
| n1 | 2^(m+1) - 1 | 2^(m+2) - 1 |
| n2 | 2^(m+2) - 1 | 3*2^(m+1) - 1 |
| n3 | 2^(m+3) - 1 | 2^(m+3) - 1 |
m =
If m is even:
If m is odd:
| n1 = | 2^(m+1) - 1 = | {{n1()}} |
| n2 = | 2^(m+2) - 1 = | {{n2()}} |
| n3 = | 2^(m+3) - 1 = | {{n3()}} |
| n1 = | 2^(m+2) - 1 = | {{n1()}} |
| n2 = | 3*2^(m+1) - 1 = | {{n2()}} |
| n3 = | 2^(m+3) - 1 = | {{n3()}} |
Calculating for {{ start }}...
| {{rowIndex/2}} | |
| n1 Collatz sequence | {{value}} |
|---|---|
| n2 Collatz sequence | {{value}} |
| n3 Collatz sequence | {{value}} |