Template:Sequence of the Day for August 27

Intended for: August 27, 2011

Timetable

• First draft entered by Alonso del Arte on May 27, 2011 as a verbatim copy of a write-up from December 27, 2010 ✓
• Draft reviewed by Alonso del Arte on August 21, 2011 ✓
• Draft approved by NOT AL on August 2?, 2011

Yesterday's SOTD * Tomorrow's SOTD

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A008884: Collatz trajectory starting at 27 (see Collatz problem).

{ 27, 82, 41, 124, 62, 31, 94, ... }

With the familiar Collatz function

f  (n) = n 2

if

n

is even and

f  (n) = 3n + 1

if

n

is odd, we still can’t say for sure whether or not every starting value of the iterated function eventually reaches 1. Often we can’t even look at a random number and be able to tell how long it takes to reach 1: some numbers reach 1 fairly quickly (numbers like 5 and 341), while others go on a long, wild ride. Such is the case with 27. Term visibility in the main OEIS entry caps this sequence at the 62^nd iteration, which has gotten up to 1079 (having hit some even higher values earlier on). In the b-file we see that the sequence later on reaches 9232 at the 77^th iteration, and finally hits 16 at the 107^th. Kind of amazing, or maybe not, that it did not hit a higher power of four (can only hit even powers of two).