Jon Seymour <a_beautiful_k@wildducktheories.com>
14 October 2023 (updated: 22 October 2023)
"Mathematics may not be ready for such problems" - Paul Erdős on the Collatz conjecture.
It has long been known that the following identity applies to all paths of the Collatz sequence.
where
This paper derives a formula for k derived from 3 parameter sequences
The resultant identity is not novel, for example see [1], but perhaps the technique by which it was derived may be interesting to some.
We also derive a recurrence relation that expresses each
and show that
[1] First odd term of the sequence lower odd number $n$ related to the $3\cdot n+1$ on Maths Overflow Net
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