Audioactive Sequence

Post Reply
User avatar
Royal
Posts: 10562
Joined: Mon Apr 11, 2011 5:55 pm

Audioactive Sequence

Post by Royal » Fri Mar 02, 2012 9:58 am

Consider the following sequence of numbers: 1, 11, 21, 1211, 111221,... To appreciate how the sequence is formed, it helps to speak the entries in each row out loud. The second entry has two "ones" thereby giving the 21 for the third entry. The third entry has one "two" and one "one". Extending the pattern, and entire sequence can be generated. The sequence was extensively studied by mathematician John Conway, who called the process audio active.

The strange construction method for the audioactive process yields Conway's constant, 1.3035...., which turns out to be a unique positive real root of a 69-term polynomial equation. This root is at the location of the red dot. Other roots of this polynomial are shown as blue dots.

Post Reply