Look-and-say sequence

The Conway result is named after the British mathematician John Horton Conway mathematical result. It was first published in 1986 by John Conway. (Lit.: Conway, 1986).

The Conway sequence is found very often again as a puzzle task. In this case, usually the first few terms of the sequence are disclosed and asked the mystery candidate to continue the sequence. Due to the rather unusual definition of the consequence this has some potential for headaches.

Definition

The terms of the sequence defined recursively on one for the mathematics rather curious way. The links here are not to be considered in the proper sense as numbers in the decimal system, but merely as sequences of digits from their description in each case the successor sequence of digits is determined. Starting value is always a positive integer (or any sequence of digits ), usually. To determine the follower one determines the maximum length of the blocks of the same digits in the previous number, and writes the frequency and number for each block row. The number is written as the next follower. If the Start value no other digit is included or a sufficiently long sequence of the same digits (for example, 11111 ) occurs, there are all the members of the Conway sequence of the digits 1, 2 and 3

Illustration of the definition of

Conway sequence for different initial values

Mathematical properties

• The length of the sequence diverges for all initial values ​​except the 22 against and growing very fast. The decimal representation of the 70th follower for already 179 691 598 places. Asymptotically increases the length of the sequence elements with the speed. Herein, the so-called Conway 's constant.
• For contrast, all members of the sequence are identical, so it is stationary.
• For (and many other values) the result always contains only the digits 1, 2 and 3, which never occurs, the sequence of digits.