Science Fair Project Encyclopedia
Look and Say sequence
In mathematics, the look and say sequence is the sequence of integers beginning as follows:
- 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...
To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. For example:
- 1 is read off as "one 1" that is, 11.
- 11 is read off as "two 1's" that is, 21.
- 21 is read off as "one 2, then one 1" that is, 1211.
- 1211 is read off as "one 1, then one 2, then two 1's" that is, 111221.
- 111221 is read off as "three 1, then two 2, then one 1" that is 312211.
The idea is similar to that of run-length encoding.
Properties
This sequence was first introduced by John Conway in 1987 under the name "audioactive decay". In the same paper Conway also proved that, if Li is the length of the sequence on the ith iteration:
where 
is an algebraic number of degree 71 known as Conway's constant. This property also holds for all variants of the Look and Say sequence defined by beginning with a different number (e.g. 13, 1113, 3113, 132113...), except for the degenerate case 22, 22, 22, 22....
External links
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