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Describe the previous term! (method A - initial term is 3).
(Formerly M2965)
27

%I M2965 #51 Aug 03 2024 02:29:32

%S 3,13,1113,3113,132113,1113122113,311311222113,13211321322113,

%T 1113122113121113222113,31131122211311123113322113,

%U 132113213221133112132123222113,11131221131211132221232112111312111213322113,31131122211311123113321112131221123113111231121123222113

%N Describe the previous term! (method A - initial term is 3).

%C Method A = 'frequency' followed by 'digit'-indication.

%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="/A006715/b006715.txt">Table of n, a(n) for n=1..20</a>

%H Éric Brier, Rémi Géraud-Stewart, David Naccache, Alessandro Pacco, and Emanuele Troiani, <a href="https://arxiv.org/abs/2006.06837">Stuttering Conway Sequences Are Still Conway Sequences</a>, arXiv:2006.06837 [math.DS], 2020.

%H Éric Brier, Rémi Géraud-Stewart, David Naccache, Alessandro Pacco, and Emanuele Troiani, <a href="https://arxiv.org/abs/2006.07246">The Look-and-Say The Biggest Sequence Eventually Cycles</a>, arXiv:2006.07246 [math.DS], 2020.

%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>.

%e The term after 3113 is obtained by saying "one 3, two 1's, one 3", which gives 132113.

%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, 3 ][ [ n ] ]; Table[ FromDigits[ F[ n ] ], {n, 11} ] (* _Zerinvary Lajos_, Mar 21 2007 *)

%o (Perl)

%o # This outputs the first n elements of the sequence, where n is given on the command line.

%o $s = 3;

%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

%Y Cf. A001140, A001141, A001143, A001145, A001151, A001154, A001155, A005150, A006751.

%Y Cf. A088204 (continuous version).

%K nonn,base,easy,nice

%O 1,1

%A _N. J. A. Sloane_