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Template:Sequence of the Day for August 27

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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).