A240595 Look-and-Say table, where in row(n+1) the sorted list of distinct terms of row(n) is preceded by the list of numbers of their occurrences.

1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 2, 2, 1, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 2, 2, 2, 1, 2, 3, 1, 4, 1, 1, 2, 3, 3, 1, 1, 1, 1, 2, 3, 4, 4, 1, 2, 1, 1, 2, 3, 4, 3, 2, 1, 2, 1, 2, 3, 4, 2, 3, 2, 1, 1, 2, 3, 4, 2, 3, 2, 1, 1, 2, 3, 4, 2, 3, 2, 1, 1, 2, 3, 4, 2

Offset: 1

Author

Reinhard Zumkeller, Apr 08 2014

Keywords

• nonn
• tabf

Comments

For n > 13: row(n) = row(13), see example.

Examples

			.  1: [1] -> 1x1 -> [1 | 1] -> row(2)
.  2: [1,1] -> 2x1 -> [2 | 1] -> row(3)
.  3: [2,1] -> 1x1, 1x2 -> [1,1 | 1,2] -> row(4)
.  4: [1,1,1,2] -> 3x1, 1x2 -> [3,1 | 1,2] -> row(5)
.  5: [3,1,1,2] -> 2x1, 1x2, 1x3 -> [2,1,1 | 1,2,3] -> row(6)
.  6: [2,1,1,1,2,3] -> 3x1, 2x2, 1x3 -> [3,2,1 | 1,2,3] -> row(7)
.  7: [3,2,1,1,2,3] -> 2x1, 2x2, 2x3 -> [2,2,2 | 1,2,3] -> row(8)
.  8: [2,2,2,1,2,3] -> 1x1, 4x2, 1x3 -> [1,4,1 | 1,2,3] -> row(9)
.  9: [1,4,1,1,2,3] -> 3x1, 1x2, 1x3, 1x4 -> [3,1,1,1 | 1,2,3] -> row(10)
. 10: [3,1,1,1,1,2,3,4] -> 4x1, 1x2, 2x3, 1x4 -> [4,1,2,1 | 1,2,3,4]
. 11: [4,1,2,1,1,2,3,4] -> 3x1, 2x2, 1x3, 2x4 -> [3,2,1,2 | 1,2,3,4]
. 12: [3,2,1,2,1,2,3,4] -> 2x1, 3x2, 2x3, 1x4 -> [2,3,2,1 | 1,2,3,4]
. 13: [2,3,2,1,1,2,3,4] -> 2x1, 3x2, 2x3, 1x4 -> [2,3,2,1 | 1,2,3,4]
. 14: [2,3,2,1,1,2,3,4] = row(13).
		

Links

• Eric Weisstein's World of Mathematics, Look and Say Sequence
• Wikipedia, Look-and-say sequence

Crossrefs

Cf. A034002.

Programs

Haskell

import Data.List (sort, group)
a240595 n k = a240595_tabf !! (n-1) !! (k-1)
a240595_row n = a240595_tabf !! (n-1)
a240595_tabf = iterate f [1] where
   f xs = concat [map length zss, map head zss]
          where zss = group $ sort xs