A088203 Infinite audioactive word that shifts 1 place left under "Look and Say" method A, starting with a(1)=2.

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

Offset: 1

Author

Paul D. Hanna, Sep 22 2003

Keywords

• nonn
• easy
• tabf

Comments

A006751(n) = concatenation of n-th row. - Reinhard Zumkeller, Aug 09 2012

From Jean-Christophe Hervé, May 07 2013: (Start)

The sequence is obtained continuously by applying the look-and-say rule from seed 2: 2 -> 1,2 -> 1,1,1,2 -> etc. The sequence is then determined by pairs of digits. Terms of even ranks are counts while odd ranks are figures. A225224 and A221646 are from seed 1 and A088204 from seed 3.

The present sequence is the concatenation of A006751 (original look-and-say method by blocks) because, with seed 2, all blocks of A006751 begin with 1 or 3 and end with 2 and therefore, there is no possible interaction between blocks after concatenation. (End)

References

• J. H. Conway, The weird and wonderful chemistry of audioactive decay, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 173-188.

Links

• Reinhard Zumkeller, Rows n = 1..25 of triangle, flattened
• Kevin Watkins, Abstract Interpretation Using Laziness: Proving Conway's Lost Cosmological Theorem,
• Kevin Watkins, Proving Conway's Lost Cosmological Theorem, POP seminar talk, CMU, Dec 2006
• Eric Weisstein's World of Mathematics, Look and Say Sequence
• Wikipedia, Look-and-say sequence

Crossrefs

Cf. A088204, A087282, A005150.

Cf. A034002, A005150, A006751.

Cf. A225224, A221646 (seed one).

Programs

Haskell

-- see Watkins link, p. 3.
import Data.List (group)
a088203 n k = a088203_tabf !! (n-1) !! (k-1)
a088203_row n = a088203_tabf !! (n-1)
a088203_tabf = iterate
               (concat . map (\xs -> [length xs, head xs]) . group) [2]
-- Reinhard Zumkeller, Aug 09 2012