

A294689


Collatz cycle of negative numbers starting with 17.


0



17, 25, 37, 55, 82, 41, 61, 91, 136, 68, 34, 17, 25, 37, 55, 82, 41, 61, 91, 136, 68, 34, 17, 25, 37, 55, 82, 41, 61, 91, 136, 68, 34, 17, 25, 37, 55, 82, 41, 61, 91, 136, 68, 34
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

This is the longest of the three known cycles of negative numbers under the reduced Collatz transformation x: x=x/2 when x is even, and x=(3x+1)/2 when x is odd. The other two cycles of negative numbers are (1,1,1,...) and (5,7,10,5,7,10,...). Only one cycle of positive numbers is known: (1,2,1,2,...). (0,0,0,...) is also a cycle.


LINKS

Table of n, a(n) for n=1..44.
Eric Weisstein's World of Mathematics, Collatz Problem
Wikipedia, Collatz conjecture


FORMULA

a(1) = 17, a(n+1) = A123684(abs(a(n))).
a(n+11) = a(n).


CROSSREFS

Positive number transforms are in A014682; the absolute value of negative number transforms can be found in A123684.
Sequence in context: A140609 A131275 A227238 * A263540 A183346 A166666
Adjacent sequences: A294686 A294687 A294688 * A294690 A294691 A294692


KEYWORD

sign,easy


AUTHOR

Joe Slater, Nov 07 2017


STATUS

approved



