In mathematics, the look and say sequence is the sequence of integers beginning as follows: Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... This is a page about mathematics. ... The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. ...

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. Run-length encoding (RLE) is a very simple form of data compression in which runs of data (that is, sequences in which the same data value occurs in many consecutive data elements) are stored as a single data value and count, rather than as the original run. ...

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: John Horton Conway (born December 26, 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. ...

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.... In mathematics, an algebraic number relative to a field F is any element x of a given field K containing F such that x is a solution of a polynomial equation of the form anxn + an−1xn−1 + ··· + a1x + a0 = 0 where n is a positive integer called the degree... In mathematics, a degenerate case is a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. ...

External links

• On-Line Encyclopedia of Integer Sequences
• MathWorld
• Look and Say sequence generator