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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 ...
In the original Collatz sequence, the successor of n is either n / 2 (for even n) or 3n + 1 (for odd n). The value 3n + 1 is clearly even for odd n, hence the next term after 3n + 1 is surely 3n + 1 / 2 . In the sequence computed by the tag system below we skip this intermediate step, hence the successor of n is 3n + 1 / 2 ...
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1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, ... For n ≥ 2, a ( n ) is the prime that is finally reached when you start with n , concatenate its prime factors (A037276) and repeat until a prime is reached; a ( n ) = −1 if no prime is ever reached.
The following other wikis use this file: Usage on ca.wikipedia.org Conjectura de Collatz; Usage on eu.wikipedia.org Collatzen aierua; Usage on fr.wikipedia.org
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The following other wikis use this file: Usage on ca.wikipedia.org Conjectura de Collatz; Usage on eu.wikipedia.org Collatzen aierua; Usage on fi.wikipedia.org
The sequence of gaps between consecutive prime numbers has a finite lim inf. See Polymath Project#Polymath8 for quantitative results. 2013: Adam Marcus, Daniel Spielman and Nikhil Srivastava: Kadison–Singer problem: functional analysis: The original problem posed by Kadison and Singer was not a conjecture: its authors believed it false.