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 L_i is the length of the sequence on the ith iteration:

:frac{L_{i+1}}{L_{i}} ightarrow lambda

where lambda = 1.303577269ldots 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 degeneracy (mathematics) case 22, 22, 22, 22....

= External links =