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A006751 Describe the previous term! (method A - initial term is 2).
(Formerly M2052)
29
2, 12, 1112, 3112, 132112, 1113122112, 311311222112, 13211321322112, 1113122113121113222112, 31131122211311123113322112, 132113213221133112132123222112, 11131221131211132221232112111312111213322112, 31131122211311123113321112131221123113111231121123222112 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
REFERENCES
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.
LINKS
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
FORMULA
a(n+1) = A045918(a(n)). - Reinhard Zumkeller, Aug 09 2012
EXAMPLE
E.g. the term after 3112 is obtained by saying "one 3, two 1's, one 2", which gives 132112.
MATHEMATICA
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 *)
PROG
(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.append(int(y))
y=''
s=1
print(l) # Indranil Ghosh, Jul 05 2017
CROSSREFS
Cf. A088203 (continuous version).
Sequence in context: A057120 A345976 A112512 * A023989 A001389 A022914
KEYWORD
nonn,base,easy,nice
AUTHOR
STATUS
approved

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Last modified April 13 18:35 EDT 2024. Contains 371644 sequences. (Running on oeis4.)