Template:Sequence of the Day for June 25

Intended for: June 25, 2013

Timetable

• First draft entered by Alonso del Arte on March 28, 2012 ✓
• Draft reviewed by Daniel Forgues on May 30, 2012 ✓
• Draft approved by May 25, 2013

Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.

---

A008908: Number of halving and tripling steps to reach 1 in the 3x + 1 problem.

{ 1, 2, 8, 3, 6, 9, 17, 4, 20, 7, 15, 10, 10, ... }

What is so fascinating about this sequence is that it looks so random, and yet there is a precise method to determine its terms. Though the question remains whether or not there is a term that is actually null (that is to say, that 1 is never reached), due to either

• the process entering a loop (of finite length) after a finite number of steps;
• the process growing without bounds [might one say: entering a loop (of infinite length) after a finite number of steps? (this would allow merging the two potentialities into one!)].