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

%I A088203 #29 Aug 14 2025 20:22:32
%S A088203 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,
%T A088203 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,
%U A088203 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
%N A088203 Infinite audioactive word that shifts 1 place left under "Look and Say" method A, starting with a(1)=2.
%C A088203 A006751(n) = concatenation of n-th row. - _Reinhard Zumkeller_, Aug 09 2012
%C A088203 From _Jean-Christophe Hervé_, May 07 2013: (Start)
%C A088203 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.
%C A088203 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)
%D A088203 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.
%H A088203 Reinhard Zumkeller, <a href="/A088203/b088203.txt">Rows n = 1..25 of triangle, flattened</a>
%H A088203 Kevin Watkins, <a href="http://www.cs.cmu.edu/~kw/pubs/conway.pdf">Abstract Interpretation Using Laziness: Proving Conway's Lost Cosmological Theorem, </a>
%H A088203 Kevin Watkins, <a href="http://www.cs.cmu.edu/~kw/pubs/conwayslides.pdf">Proving Conway's Lost Cosmological Theorem, POP seminar talk, CMU, Dec 2006</a>
%H A088203 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LookandSaySequence.html">Look and Say Sequence</a>
%H A088203 Wikipedia, <a href="http://en.wikipedia.org/wiki/Look-and-say_sequence">Look-and-say sequence</a>
%o A088203 (Haskell) -- see Watkins link, p. 3.
%o A088203 import Data.List (group)
%o A088203 a088203 n k = a088203_tabf !! (n-1) !! (k-1)
%o A088203 a088203_row n = a088203_tabf !! (n-1)
%o A088203 a088203_tabf = iterate
%o A088203                (concat . map (\xs -> [length xs, head xs]) . group) [2]
%o A088203 -- _Reinhard Zumkeller_, Aug 09 2012
%Y A088203 Cf. A088204, A087282, A005150.
%Y A088203 Cf. A034002, A005150, A006751.
%Y A088203 Cf. A225224, A221646 (seed one).
%K A088203 nonn,easy,tabf
%O A088203 1,1
%A A088203 _Paul D. Hanna_, Sep 22 2003