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URL: https://oeis.org/A224254

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A224254
Full cycle lengths in the Collatz (3x+1) problem when the negative integers are used.
2
2, 2, 2, 2, 5, 2, 5, 2, 5, 5, 2, 2, 5, 5, 2, 2, 18, 5, 5, 5, 18, 2, 18, 2, 18, 5, 5, 5, 2, 2, 18, 2, 18, 18, 5, 5, 18, 5, 2, 5, 18, 18, 2, 2, 18, 18, 5, 2, 18, 18, 5, 5, 2, 5, 18, 5, 2, 2, 2, 2, 18, 18, 5, 2, 2, 18, 18, 18, 2, 5, 2, 5, 18, 18, 5, 5, 2, 2, 2, 5, 5
OFFSET
1,1
COMMENTS
There are other cycles of lengths 2, 5 and 18 if negative integers are used. In Z, it is conjectured that the five values of cycle are 1, 2, 3, 5 and 18 (see A121510).
EXAMPLE
a(1) = 2 because the cycle -1 -> -2 -> -1... contains 2 distinct terms;
a(5) = 5 because the cycle -5 -> -14 -> -7->-20 -> -5 ... contains 5 distinct terms;
a(17) = 18 because the cycle -17 -> -50 -> -25->-74 -> -37 -> -110 -> -55->-164 -> -82 -> -41 -> -122->-61 -> -182 -> -91 -> -272->-136 -> -68 -> -34 -> -17... contains 18 distinct terms.
PROG
(Python)
import sympy
def A224254(n):
return next(sympy.cycle_length(lambda x:3*x+1 if x%2 else x//2, -n))[0] # Pontus von Brömssen, Jan 24 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Apr 02 2013
EXTENSIONS
Data corrected by Pontus von Brömssen, Jan 24 2021
STATUS
approved