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Which operation is performed, 3n + 1 / 2 or n / 2 , depends on the parity. The parity sequence is the same as the sequence of operations. Using this form for f(n), it can be shown that the parity sequences for two numbers m and n will agree in the first k terms if and only if m and n are equivalent modulo 2 k. This implies that ...
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
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Lothar Collatz (German:; July 6, 1910 – September 26, 1990) was a German mathematician, born in Arnsberg, Westphalia. The "3x + 1" problem is also known as the Collatz conjecture, named after him and still unsolved. The Collatz–Wielandt formula for the Perron–Frobenius eigenvalue of a positive square matrix was also named after him.
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 ...
Directed graph showing the orbits of the first 1000 numbers in the Collatz conjecture. The integers from 1 to 1000 are colored from red to violet according to their ...
The parity sequences discussed can, of course, be played in reverse giving you similar equations. Also, check the references for "Blueprint for Failure: How to Construct a Counterexample to the Collatz Conjecture". In that paper (by yours truly) is an equation system similar to the parity sequences.
The following other wikis use this file: Usage on ar.wikipedia.org حدسية كولاتز; Usage on ca.wikipedia.org Conjectura de Collatz; Usage on cs.wikipedia.org