1,1

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

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.

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

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

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

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 *)

(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

(Python)

from functools import cache

from itertools import groupby

def LS(n): return int(''.join(str(len(list(g)))+k for k, g in groupby(str(n))))

@cache

def a(n): return 2 if n == 1 else LS(a(n-1))

print([a(n) for n in range(1, 14)]) # Michael S. Branicky, Jan 10 2026

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

Cf. A088203 (continuous version).

Sequence in context: A057120 A345976 A112512 * A023989 A001389 A022914

Adjacent sequences: A006748 A006749 A006750 * A006752 A006753 A006754

nonn,base,easy,nice,changed

approved