Search: id:A005150
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%I A005150 M4780
%S A005150 1,11,21,1211,111221,312211,13112221,1113213211,31131211131221,
%T A005150 13211311123113112211,11131221133112132113212221,
%U A005150 3113112221232112111312211312113211
%N A005150 Look and Say sequence: describe the previous term! (method A - initial 
               term is 1).
%C A005150 Method A = 'frequency' followed by 'digit'-indication.
%C A005150 Only the digits 1, 2 and 3 appear in any term. - Robert G. Wilson v Jan 
               22 2004.
%D A005150 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005150 J. H. Conway, The weird and wonderful chemistry of audioactive decay, 
               Eureka 46 (1986) 5-16.
%D A005150 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.
%D A005150 S. B. Ekhad and D. Zeilberger, Proof of Conway's lost cosmological theorem, 
               Elect. Res. Announcements Amer, Math. Soc., 3 (1997), 78-82.
%D A005150 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.
%D A005150 O. Martin, Look-and-Say Biochemistry: Exponential RNA and Multistranded 
               DNA, Amer. Math. Monthly, 113 (No. 4, 2006), 289-307.
%D A005150 Clifford A. Pickover, Fractal horizons : the future use of fractals, 
               New York : St. Martin's Press, 1996. ISBN 0312125992. Chapter 7 has 
               an extensive description of the elements and their properties.
%D A005150 J. Sauerberg and L. Shu, The long and the short on counting sequences, 
               Amer. Math. Monthly, 104 (1997), 306-317.
%D A005150 James J. Tattersall, Elementary Number Theory in Nine Chapters, 1999, 
               p. 23.
%D A005150 I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood 
               City, CA, 1991, p. 4.
%D A005150 C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 486.
%H A005150 T. D. Noe, <a href="b005150.txt">Table of n, a(n) for n = 1..25</a>
%H A005150 Henry Bottomley, <a href="http://www.btinternet.com/~se16/js/lands2.htm">
               Evolution of Conway's 92 Look and Say audioactive elements</a>
%H A005150 S. R. Finch, <a href="http://algo.inria.fr/bsolve/constant/cnwy/cnwy.html">
               Conway's Constant</a>
%H A005150 M. Hilgemeier, <a href="http://www.btinternet.com/~se16/mhi">One metaphor 
               fits all</a>, in Fractal Horizons, ed. C. A Pickover, St. Martins, 
               NY, 1996, pp. 137-161.
%H A005150 R. A. Litherland, <a href="http://www.math.lsu.edu/~lither/jhc/doc.pdf">
               The audioactive package</a>
%H A005150 R. A. Litherland, <a href="http://www.math.lsu.edu/~lither/jhc/cct.pdf">
               Conway's cosmological theorem</a>
%H A005150 M. Lothaire, <a href="http://www-igm.univ-mlv.fr/~berstel/Lothaire/">
               Algebraic Combinatorics on Words</a>, Cambridge, 2002, see p. 37, 
               etc.
%H A005150 Paulo Ortolan, <a href="a005150.txt">Java program for A005150</a>
%H A005150 T. Sillke, <a href="http://www.mathematik.uni-bielefeld.de/~sillke/SEQUENCES/
               series000">Conway sequence</a>
%H A005150 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LookandSaySequence.html">Link to a section of The World of Mathematics.</
               a>
%H A005150 D. Zeilberger, <a href="http://arXiv.org/abs/math.CO/9808077">[math/9808077] 
               Proof of Conway's Lost Cosmological Theorem</a>
%H A005150 D. Zeilberger, <a href="http://www.ams.org/era/1997-03-11/S1079-6762-97-00026-7/
               home.html">Proof of Conway's lost cosmological theorem</a>, Electron. 
               Res. Announc. Amer. Math. Soc. 3 (1997), 78-82.
%e A005150 E.g. the term after 1211 is obtained by saying "one 1, one 2, two 1's", 
               which gives 111221.
%t A005150 RunLengthEncode[ x_List ] := (Through[ {First, Length}[ #1 ] ] &) /@ 
               Split[ x ]; LookAndSay[ n_, d_:1 ] := NestList[ Flatten[ Reverse 
               /@ RunLengthEncode[ # ] ] &, {d}, n - 1 ]; F[ n_ ] := LookAndSay[ 
               n, 1 ][ [ n ] ]; Table[ FromDigits[ F[ n ] ], {n, 1, 15} ]
%o A005150 (Haskell program from Josh Triplett (josh(AT)freedesktop.org), Jan 03 
               2007)
%o A005150 import List
%o A005150 say :: Integer -> Integer
%o A005150 say = read . concatMap saygroup . group . show
%o A005150 where saygroup s = (show $ length s) ++ [head s]
%o A005150 look_and_say :: [Integer]
%o A005150 look_and_say = 1 : map say look_and_say
%o A005150 (Java) See Paulo Ortolan link.
%o A005150 (PERL) #!/usr/bin/perl $str="1"; for (1 .. shift(@ARGV)) { print($str, 
               ","); @a = split(//,$str); $str=""; $nd=shift(@a); while (defined($nd)) 
               { $d=$nd; $cnt=0; while (defined($nd) && ($nd eq $d)) { $cnt++; $nd 
               = shift(@a); } $str .= $cnt.$d; } } print($str);
%o A005150 (PERL - better program from Arne 'Timwi' Heizmann (timwi(AT)gmx.net), 
               Mar 12 2008)
%o A005150 # This outputs the first n elements of the sequence, where n is given 
               on the command line.
%o A005150 $s = 1;
%o A005150 for (2..shift @ARGV) {
%o A005150 print "$s, ";
%o A005150 $s =~ s/(.)\1*/(length $&).$1/eg;
%o A005150 }
%o A005150 print "$s\n";
%o A005150 (Python, from Olivier Mengue (dolmen(AT)users.sourceforge.net), Jul 01 
               2005: replace leading dots by blanks before running)
%o A005150 .def A005150(n):
%o A005150 ... p = "1"
%o A005150 ... seq = [1]
%o A005150 ... while (n > 1):
%o A005150 ....... q = ''
%o A005150 ....... idx = 0 # Index
%o A005150 ....... l = len(p) # Length
%o A005150 ....... while idx < l:
%o A005150 ........... start = idx
%o A005150 ........... idx = idx + 1
%o A005150 ........... while idx < l and p[idx] == p[start]:
%o A005150 ............... idx = idx + 1
%o A005150 ........... q = q + str(idx-start) + p[start]
%o A005150 ....... n, p = n - 1, q
%o A005150 ....... seq.append(int(p))
%o A005150 ... return seq
%o A005150 (A second Python program from E. Johnson (ejohnso9(AT)earthlink.net), 
               Mar 31 2008: replace leading dots by blanks before running)
%o A005150 .def A005150(n):
%o A005150 ... seq = [1] + [None] * (n - 1) # allocate entire array space
%o A005150 ... def say(s):
%o A005150 ....... acc = '' # initialize accumulator
%o A005150 ....... while len(s) > 0:
%o A005150 ........... i = 0
%o A005150 ........... c = s[0] # char of first run
%o A005150 ........... while (i < len(s) and s[i] == c): # scan first digit run
%o A005150 ............... i += 1
%o A005150 ........... acc += str(i) + c # append description of first run
%o A005150 ........... if i == len(s):
%o A005150 ............... break # done
%o A005150 ........... else:
%o A005150 ............... s = s[i:] # trim leading run of digits
%o A005150 ....... return acc
%o A005150 ... for i in xrange(1, n):
%o A005150 ....... seq[i] = int(say(str(seq[i-1])))
%o A005150 ... return seq
%Y A005150 Cf. A001155, A006751, A006715, A001140, A001141, A001143, A001145, A001151, 
               A001154, A007651.
%Y A005150 Cf. A001387. Length of n-th term = A005341. Periodic table: A119566.
%Y A005150 Sequence in context: A158081 A007890 A063850 this_sequence A001388 A110393 
               A064263
%Y A005150 Adjacent sequences: A005147 A005148 A005149 this_sequence A005151 A005152 
               A005153
%K A005150 nonn,base,easy,nice
%O A005150 1,2
%A A005150 N. J. A. Sloane (njas(AT)research.att.com).
%E A005150 Perl program from Jeff Quilici (jeff(AT)quilici.com), Aug 12 2003

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