

A006751


Describe the previous term! (method A  initial term is 2).
(Formerly M2052)


27



2, 12, 1112, 3112, 132112, 1113122112, 311311222112, 13211321322112, 1113122113121113222112, 31131122211311123113322112, 132113213221133112132123222112, 11131221131211132221232112111312111213322112, 31131122211311123113321112131221123113111231121123222112
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OFFSET

1,1


COMMENTS

Method A = 'frequency' followed by 'digit'indication.
No digit exceeds 3. If the starting number a(1) is a singledigit 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 nth row in A088203.  Reinhard Zumkeller, Aug 09 2012
This is because for all n > 1, a(n) begins by 1 or 3 and ends by 2. [JeanChristophe HervĂ©, 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. 452455.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
I. Vardi, Computational Recreations in Mathematica. AddisonWesley, Redwood City, CA, 1991, p. 4.


LINKS

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. 173188.
S. R. Finch, Conway's Constant [Broken link]
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)


CROSSREFS

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


KEYWORD

nonn,base,easy,nice


AUTHOR

N. J. A. Sloane


STATUS

approved



