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

1,1

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 W. Weisstein, MathWorld: Look and Say Sequence

Wikipedia, Look-and-say sequence

Prog

(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

Crossrefs

Cf. A088204, A087282, A005150.

Cf. A034002, A005150, A006751

Cf. A225224, A221646 (seed one).

Sequence in context: A140816 A029433 A337144 * A205649 A176510 A362951

Adjacent sequences: A088200 A088201 A088202 * A088204 A088205 A088206

Keyword

nonn,easy,tabf

Author

Paul D. Hanna, Sep 22 2003

Status

approved