A006751 Describe the previous term! (method A - initial term is 2).

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy
• nice

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

Examples

			E.g. the term after 3112 is obtained by saying "one 3, two 1's, one 2", which gives 132112.
		

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

• 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

Crossrefs

Cf. A001140, A001141, A001143, A001145, A001151, A001154, A001155, A005150, A006715, A045918.

Cf. A088203 (continuous version).

Programs

Haskell

a006751 = foldl1 (\v d -> 10 * v + d) . map toInteger . a088203_row
-- Reinhard Zumkeller, Aug 09 2012

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 *)

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

Formula

a(n+1) = A045918(a(n)). - Reinhard Zumkeller, Aug 09 2012