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%I M2052 #67 Feb 20 2023 12:27:49
%S 2,12,1112,3112,132112,1113122112,311311222112,13211321322112,
%T 1113122113121113222112,31131122211311123113322112,
%U 132113213221133112132123222112,11131221131211132221232112111312111213322112,31131122211311123113321112131221123113111231121123222112
%N Describe the previous term! (method A - initial term is 2).
%C Method A = 'frequency' followed by 'digit'-indication.
%C No digit exceeds 3. If the starting number a(1) is a single-digit number greater than 3 this will remain as the last digit, all the remaining in any term being no greater than 3. - _Carmine Suriano_, Sep 07 2010
%C a(n) = value of concatenation of n-th row in A088203. - _Reinhard Zumkeller_, Aug 09 2012
%C This is because for all n > 1, a(n) begins with 1 or 3 and ends with 2. - _Jean-Christophe Hervé_, May 07 2013
%C a(n+1) - a(n) is divisible by 10^5 for n > 5. - _Altug Alkan_, Dec 04 2015
%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 4.
%H T. D. Noe, <a href="/A006751/b006751.txt">Table of n, a(n) for n=1..20</a>
%H J. H. Conway, <a href="http://dx.doi.org/10.1007/978-1-4612-4808-8_53">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.
%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/cnwy/cnwy.html">Conway's Constant</a> [Broken link]
%H S. R. Finch, <a href="http://web.archive.org/web/20010207194413 /http://www.mathsoft.com/asolve/constant/cnwy/cnwy.html">Conway's Constant</a> [From the Wayback Machine]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LookandSaySequence.html">Look and Say Sequence</a>
%F a(n+1) = A045918(a(n)). - _Reinhard Zumkeller_, Aug 09 2012
%e E.g. the term after 3112 is obtained by saying "one 3, two 1's, one 2", which gives 132112.
%t RunLengthEncode[ x_List ] := (Through[ {First, Length}[ #1 ] ] &) /@ Split[ x ]; LookAndSay[ n_, d_:1 ] := NestList[ Flatten[ Reverse /@ RunLengthEncode[ # ] ] &, {d}, n - 1 ]; F[ n_ ] := LookAndSay[ n, 2 ][ [ n ] ]; Table[ FromDigits[ F[ n ] ], {n, 11} ] (* _Zerinvary Lajos_, Mar 21 2007 *)
%o (Haskell)
%o a006751 = foldl1 (\v d -> 10 * v + d) . map toInteger . a088203_row
%o -- _Reinhard Zumkeller_, Aug 09 2012
%o (Perl)
%o # This outputs the first n elements of the sequence, where n is given on the command line.
%o $s = 2;
%o for (2..shift @ARGV) {
%o print "$s, ";
%o $s =~ s/(.)\1*/(length $&).$1/eg;
%o }
%o print "$s\n";
%o ## Arne 'Timwi' Heizmann (timwi(AT)gmx.net), Mar 12 2008)
%o (Python)
%o l=[2]
%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 y=''
%o s=1
%o print(l) # _Indranil Ghosh_, Jul 05 2017
%Y Cf. A001140, A001141, A001143, A001145, A001151, A001154, A001155, A005150, A006715, A045918.
%Y Cf. A088203 (continuous version).
%K nonn,base,easy,nice
%O 1,1
%A _N. J. A. Sloane_
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