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Download QR code; Print/export ... result-- Return unbolded if condition not met end-- Function to handle the Collatz logic and format sequence local function ...
The sequence of numbers involved is sometimes referred to as the hailstone sequence, hailstone numbers or hailstone numerals (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), [5] or as wondrous numbers. [6] Paul Erdős said about the Collatz conjecture: "Mathematics may not be ready for such ...
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In contrast, look at how useful the heuristic is: every odd number in a Collatz sequence will be succeeded by a mean of two even numbers. Earlier, I showed how to predict the number of odd numbers in the Collatz sequence of 2**177149-1 and got an answer (853681) that was within 0.12% of the actual result of 854697.
In algebra, the 3x + 1 semigroup is a special subsemigroup of the multiplicative semigroup of all positive rational numbers. [1] The elements of a generating set of this semigroup are related to the sequence of numbers involved in the still open Collatz conjecture or the "3x + 1 problem".
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