A294689 Collatz cycle of negative numbers starting with -17.

-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

Offset: 1

Author

Joe Slater, Nov 07 2017

Keywords

• sign
• easy

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

• Eric Weisstein's World of Mathematics, Collatz Problem
• Wikipedia, Collatz conjecture

Crossrefs

Positive number transforms are in A014682; the absolute value of negative number transforms can be found in A123684.

Formula

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

a(n+11) = a(n).