A023989 Look and Say sequence: describe the previous term! (method C - initial term is 2).

2, 12, 1112, 3112, 211213, 312213, 212223, 114213, 31121314, 41122314, 31221324, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314

Offset: 0

Author

Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), Mar 19 2002

Keywords

• nonn
• base

Comments

Method C = 'frequency' followed by 'digit'-indication with digits in increasing order.

Converges to 21322314 at the eleventh term.

Depending on the initial value, the sequence may converge to a cycle of 2 or more values, for example: 123456, 111213141516, 711213141516, 61121314151617, 71121314152617, 61221314151627, 51321314152617, 51222314251617, 41421314251617, 51221334151617, 51222314251617, 41421314251617, 51221334151617. [Corrected by Pontus von Brömssen, Jun 04 2023]

a(n) = A005151(n) for n > 6. - Reinhard Zumkeller, Jan 26 2014

Examples

			a(1) = 12, so a(2) = 1112 because 12 contains a digit 1 and a digit 2; a(3) = 3112 because 1112 contains three digits 1 and a digit 2
		

Crossrefs

Cf. A005150, A005151, A022481.

Cf. A047842, A118628.

Programs

Haskell

import Data.List (group, sort, transpose)
a023989 n = a023989_list !! (n-1)
a023989_list = 2 : f [2] :: [Integer] where
   f xs = (read $ concatMap show ys) : f (ys) where
          ys = concat $ transpose [map length zss, map head zss]
          zss = group $ sort xs
-- Reinhard Zumkeller, Jan 26 2014

Formula

a(n) = A047842(a(n-1)). - Pontus von Brömssen, Jun 04 2023