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A006751
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Describe the previous term! (method A - initial term is 2).
(Formerly M2052)
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28
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2, 12, 1112, 3112, 132112, 1113122112, 311311222112, 13211321322112, 1113122113121113222112, 31131122211311123113322112, 132113213221133112132123222112, 11131221131211132221232112111312111213322112, 31131122211311123113321112131221123113111231121123222112
(list;
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OFFSET
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1,1
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COMMENTS
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Method A = 'frequency' followed by 'digit'-indication.
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
a(n) = value of concatenation of n-th row in A088203. - Reinhard Zumkeller, Aug 09 2012
This is because for all n > 1, a(n) begins with 1 or 3 and ends with 2. - Jean-Christophe Hervé, May 07 2013
a(n+1) - a(n) is divisible by 10^5 for n > 5. - Altug Alkan, Dec 04 2015
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 4.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..20
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.
S. R. Finch, Conway's Constant [Broken link]
S. R. Finch, Conway's Constant [From the Wayback Machine]
Eric Weisstein's World of Mathematics, Look and Say Sequence
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FORMULA
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a(n+1) = A045918(a(n)). - Reinhard Zumkeller, Aug 09 2012
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EXAMPLE
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E.g. the term after 3112 is obtained by saying "one 3, two 1's, one 2", which gives 132112.
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a006751 = foldl1 (\v d -> 10 * v + d) . map toInteger . a088203_row
-- Reinhard Zumkeller, Aug 09 2012
(Perl)
# This outputs the first n elements of the sequence, where n is given on the command line.
$s = 2;
for (2..shift @ARGV) {
print "$s, ";
$s =~ s/(.)\1*/(length $&).$1/eg;
}
print "$s\n";
## Arne 'Timwi' Heizmann (timwi(AT)gmx.net), Mar 12 2008)
(Python)
l=[2]
n=s=1
y=''
while n<21:
x=str(l[n - 1]) + ' '
for i in range(len(x) - 1):
if x[i]==x[i + 1]: s+=1
else:
y+=str(s)+str(x[i])
s=1
x=''
n+=1
l+=[int(y), ]
y=''
s=1
print l # Indranil Ghosh, Jul 05 2017
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CROSSREFS
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Cf. A001140, A001141, A001143, A001145, A001151, A001154, A001155, A005150, A006715, A045918.
Cf. A088203 (continuous version).
Sequence in context: A058975 A057120 A112512 * A023989 A001389 A022914
Adjacent sequences: A006748 A006749 A006750 * A006752 A006753 A006754
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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