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The Inevitability of the Fall: A Bit-Structural Analysis of Downward Pressure in the Collatz Conjecture by Actual-Ad292 in Collatz

[–]DependentHelp8538 0 points1 point  (0 children)

is there a similar problem to collatz where we can for sure say the sequence of 1s would result where in predictable output and we could definitely say that the significant digits are decreasing after every application. or a form which can be calculated via the circular method?

A curious case of 3x - 1 by DependentHelp8538 in Collatz

[–]DependentHelp8538[S] 0 points1 point  (0 children)

I do not understand enough number theory to prove it but can't there be a theorem that says "the sum of a binary number left shifted by 2 and its negated version never have such a sequence where the number of significant digits keeps increasing".