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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 ...
English: This is a graph, generated in bottom-up fashion, of the orbits of all numbers under the Collatz map with an orbit length of 20 or less. Created with Graphviz, with the help of this Python program: # This python script generates a graph that shows 20 levels of the Collatz Conjecture.
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 ...
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.
This list of sequence alignment software is a compilation of software tools and web portals ... C/C++/Python/Java SIMD dynamic programming library for SSE, AVX2: Both:
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Paul Erdős said about the Collatz conjecture: "Mathematics may not be ready for such problems."[7] Jeffrey Lagarias stated in 2010 that the Collatz conjecture "is an extraordinarily difficult problem, completely out of reach of present day mathematics".[8] FORTUNATELY, THEY WERE NOT CORRECT.