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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 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=1..81.

Wikipedia, Collatz conjecture

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

Cf. A121510, A224166, A224183.

Sequence in context: A130325 A154097 A221491 * A107604 A080647 A324516

Adjacent sequences:  A224251 A224252 A224253 * A224255 A224256 A224257

KEYWORD

nonn

AUTHOR

Michel Lagneau, Apr 02 2013

EXTENSIONS

Data corrected by Pontus von Brömssen, Jan 24 2021

STATUS

approved

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Last modified October 2 23:51 EDT 2022. Contains 357230 sequences. (Running on oeis4.)