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%I #29 Apr 08 2021 03:41:42
%S 1,1,1,2,1,1,2,1,1,1,1,1,2,2,1,3,1,2,2,1,1,1,3,1,1,2,2,2,1,1,1,1,3,2,
%T 1,3,2,1,1,3,1,1,3,1,2,1,1,1,3,1,2,2,1,1,3,2,1,1,3,1,1,1,2,3,1,1,3,1,
%U 1,2,2,1,1,1,1,1,3,1,2,2,1,1,3,3,1,1,2,1,3,2,1,1,3,2,1,2,2,2,1
%N A005150 expanded into single digits.
%C A005150(n) = Sum_{k=1..A005341(n)} T(n,k)*10^(A005341(n) - k). - _Reinhard Zumkeller_, Dec 15 2012
%H Reinhard Zumkeller, <a href="/A034002/b034002.txt">Rows n = 1..25 of triangle, flattened</a>
%H J. H. Conway, <a href="http://www.math.utah.edu/~boocher/writings/ConwayLook.pdf">The weird and wonderful chemistry of audioactive decay</a>, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 173-188. DOI: 10.1007/978-1-4612-4808-8_53.
%H M. Lothaire, <a href="http://www-igm.univ-mlv.fr/~berstel/Lothaire/">Algebraic Combinatorics on Words</a>, Cambridge, 2002, see p. 36.
%H 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 Kevin Watkins, <a href="http://www.cs.cmu.edu/~kw/pubs/conwayslides.pdf">Proving Conway's Lost Cosmological Theorem</a>, POP seminar talk, CMU, Dec 2006.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LookandSaySequence.html">Look and Say Sequence</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Look-and-say_sequence">Look-and-say sequence</a>
%e . Initial rows A005150
%e . 1: 1 1
%e . 2: 1,1 11
%e . 3: 2,1 21
%e . 4: 1,2,1,1 1211
%e . 5: 1,1,1,2,2,1 111221
%e . 6: 3,1,2,2,1,1 312211
%e . 7: 1,3,1,1,2,2,2,1 13112221
%e . 8: 1,1,1,3,2,1,3,2,1,1 1113213211
%e . 9: 3,1,1,3,1,2,1,1,1,3,1,2,2,1 31131211131221
%e -}
%o (Haskell) see Watkins link, p. 3.
%o import Data.List (group)
%o a034002 n k = a034002_tabf !! (n-1) !! (k-1)
%o a034002_row n = a034002_tabf !! (n-1)
%o a034002_tabf = iterate
%o (concat . map (\xs -> [length xs, head xs]) . group) [1]
%o -- _Reinhard Zumkeller_, Aug 09 2012
%o (Python)
%o from sympy import flatten
%o l=[1]
%o L=[1]
%o n=s=1
%o y=''
%o while n<21:
%o x=str(l[n - 1]) + ' '
%o for i in range(len(x) - 1):
%o if x[i]==x[i + 1]: s+=1
%o else:
%o y+=str(s)+str(x[i])
%o s=1
%o x=''
%o n+=1
%o l.append(int(y))
%o L.append([int(a) for a in list(y)])
%o y=''
%o s=1
%o print(l) # A005150
%o print(flatten(L)) # _Indranil Ghosh_, Jul 05 2017
%Y See the entry for A005150 for much more about this sequence.
%Y Cf. A088203.
%Y Cf. A005341 (row lengths), A220424 (method B version).
%K nonn,base,tabf
%O 1,4
%A _N. J. A. Sloane_
%E Offset changed and keyword tabf added by _Reinhard Zumkeller_, Aug 09 2012
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