A006751 -id:A006751 - cp's OEIS frontend

A005150 Look and Say sequence: describe the previous term! (method A - initial term is 1).

1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211, 11131221133112132113212221, 3113112221232112111312211312113211, 1321132132111213122112311311222113111221131221, 11131221131211131231121113112221121321132132211331222113112211, 311311222113111231131112132112311321322112111312211312111322212311322113212221

Offset: 1

N. J. A. Sloane

Method A = "frequency" followed by "digit"-indication.
Also known as the "Say What You See" sequence.
Only the digits 1, 2 and 3 appear in any term. - Robert G. Wilson v, Jan 22 2004
All terms end with 1 (the seed) and, except the third a(3), begin with 1 or 3. - Jean-Christophe Hervé, May 07 2013
Proof that 333 never appears in any a(n): suppose it appears for the first time in a(n); because of "three 3" in 333, it would imply that 333 is also in a(n-1), which is a contradiction. - Jean-Christophe Hervé, May 09 2013
This sequence is called "suite de Conway" in French (see Wikipédia link). - Bernard Schott, Jan 10 2021
Contrary to many accounts (including an earlier comment on this page), Conway did not invent the sequence. The first mention of the sequence appears to date back to the 1977 International Mathematical Olympiad in Belgrade, Yugoslavia. See the Editor's note on page 4, directly preceding Conway's article in Eureka referenced below. - Harlan J. Brothers, May 03 2024

			The term after 1211 is obtained by saying "one 1, one 2, two 1's", which gives 111221.

John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 208.
S. R. Finch, Mathematical Constants, Cambridge, 2003, section 6.12 Conway's Constant, pp. 452-455.
M. Gilpin, On the generalized Gleichniszahlen-Reihe sequence, Manuscript, Jul 05 1994.
A. Lakhtakia and C. Pickover, Observations on the Gleichniszahlen-Reihe: An Unusual Number Theory Sequence, J. Recreational Math., 25 (No. 3, 1993), 192-198.
Clifford A. Pickover, Computers and the Imagination, St Martin's Press, NY, 1991.
Clifford A. Pickover, Fractal horizons: the future use of fractals, New York: St. Martin's Press, 1996. ISBN 0312125992. Chapter 7 has an extensive description of the elements and their properties.
C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 486.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
James J. Tattersall, Elementary Number Theory in Nine Chapters, 1999, p. 23.
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..25
Henry Bottomley, Evolution of Conway's 92 Look and Say audioactive elements.
Éric Brier, Rémi Géraud-Stewart, David Naccache, Alessandro Pacco, and Emanuele Troiani, Stuttering Conway Sequences Are Still Conway Sequences, arXiv:2006.06837 [math.DS], 2020.
Éric Brier, Rémi Géraud-Stewart, David Naccache, Alessandro Pacco, and Emanuele Troiani, The Look-and-Say The Biggest Sequence Eventually Cycles, arXiv:2006.07246 [math.DS], 2020.
Onno M. Cain and Sela T. Enin, Inventory Loops (i.e. Counting Sequences) have Pre-period 2 max S_1 + 60, arXiv:2004.00209 [math.NT], 2020.
Ben Chen, Richard Chen, Joshua Guo, Tanya Khovanova, Shane Lee, Neil Malur, Nastia Polina, Poonam Sahoo, Anuj Sakarda, Nathan Sheffield, and Armaan Tipirneni, On Base 3/2 and its Sequences, arXiv:1808.04304 [math.NT], 2018.
J. H. Conway, The weird and wonderful chemistry of audioactive decay, Eureka 46 (1986) 5-16.
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.
J. H. Conway and Brady Haran, Look-and-Say Numbers (2014), Numberphile video.
S. B. Ekhad and D. Zeilberger, Proof of Conway's Lost Cosmological Theorem, arXiv:math/9808077 [math.CO], 1998.
S. B. Ekhad and D. Zeilberger, Proof of Conway's lost cosmological theorem, Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 78-82.
S. Eliahou and M. J. Erickson, Mutually describing multisets and integer partitions, Discrete Mathematics, Volume 313, Issue 4, Feb 28 2013, Pages 422-433. - From _N. J. A. Sloane_, Jan 03 2013
S. R. Finch, Conway's Constant [From the Wayback Machine]
Steven Finch, The On-Line Encyclopedia of Integer Sequences, founded in 1964 by N. J. A. Sloane, A Tribute to John Horton Conway, The Mathematical Intelligencer (2021) Vol. 43, 146-147.
X. Gourdon and B. Salvy, Effective asymptotics of linear recurrences with rational coefficients, Discrete Mathematics, vol. 153, no. 1-3, 1996, pages 145-163. See p. 161.
M. Hilgemeier, Die Gleichniszahlen-Reihe, in Bild der Wissenschaft, 12 (1986), 194-195, with permission from the Konradin Medien GmbH.
M. Hilgemeier, One metaphor fits all, in Fractal Horizons, ed. C. A Pickover, St. Martins, NY, 1996, pp. 137-161.
R. A. Litherland, Conway's Cosmological Theorem (Overview).
R. A. Litherland, Conway's Cosmological Theorem, 12 pages, Apr 14 2006 (pdf file).
R. A. Litherland, Programs for Conway's Cosmological Theorem, (gzipped tar ball).
R. A. Litherland, The audioactive package.
M. Lothaire, Algebraic Combinatorics on Words, Cambridge, 2002, see p. 37, etc.
MacTutor History of Mathematics, John H. Conway
O. Martin, Look-and-Say Biochemistry: Exponential RNA and Multistranded DNA, Amer. Math. Monthly, 113 (No. 4, 2006), 289-307. - From _N. J. A. Sloane_, Feb 19 2013
Thomas Morrill, Look, Knave, arXiv:2004.06414 [math.CO], 2020.
Paulo Ortolan, Java program for A005150.
Matt Parker, Can you trust an elegant conjecture?, Stand-Up Maths, 2022, video.
Rosetta Code, Look and say sequence programs in over 60 languages.
J. Sauerberg and L. Shu, The long and the short on counting sequences, Amer. Math. Monthly, 104 (1997), 306-317.
T. Sillke, Conway sequence.
L. J. Upton, Letter to N. J. A. Sloane, Jan 08 1991.
Kevin Watkins, Abstract Interpretation Using Laziness: Proving Conway's Lost Cosmological Theorem.
Kevin Watkins, Proving Conway's Lost Cosmological Theorem, POP seminar talk, CMU, Dec 2006.
Eric Weisstein's World of Mathematics, Look and Say Sequence.
Wikipedia, Look-and-say sequence.
Wikipédia, Suite de Conway.
W. W. Zadrozny, Abstraction, Reasoning and Deep Learning: A Study of the "Look and Say" Sequence, arXiv:2109.12755 [cs.AI], 2022.
Julia Witte Zimmerman, Denis Hudon, Kathryn Cramer, Jonathan St. Onge, Mikaela Fudolig, Milo Z. Trujillo, Christopher M. Danforth, and Peter Sheridan Dodds, A blind spot for large language models: Supradiegetic linguistic information, arXiv:2306.06794 [cs.CL], 2023.
Julia Witte Zimmerman, Denis Hudon, Kathryn Cramer, Alejandro J. Ruiz, Calla Beauregard, Ashley Fehr, Mikaela Irene Fudolig, Bradford Demarest, Yoshi Meke Bird, Milo Z. Trujillo, Christopher M. Danforth, and Peter Sheridan Dodds, Tokens, the oft-overlooked appetizer: Large language models, the distributional hypothesis, and meaning, arXiv:2412.10924 [cs.CL], 2024. See pp. 21, 28.

Cf. A001155, A006751, A006715, A001140, A001141, A001143, A001145, A001151, A001154, A007651, A060857.
Cf. A001387, Periodic table: A119566.
Cf. A225224, A221646, A225212 (continuous versions).
Apart from the first term, all terms are in A001637.
About digits: A005341 (number of digits), A022466 (number of 1's), A022467 (number of 2's), A022468 (number of 3's), A004977 (sum of digits), A253677 (product of digits).
About primes: A079562 (number of distinct prime factors), A100108 (terms that are primes), A334132 (smallest prime factor).
Cf. A014715 (Conway's constant), A098097 (terms interpreted as written in base 4).

import List
say :: Integer -> Integer
say = read . concatMap saygroup . group . show
where saygroup s = (show $ length s) ++ [head s]
look_and_say :: [Integer]
look_and_say = 1 : map say look_and_say
-- Josh Triplett (josh(AT)freedesktop.org), Jan 03 2007

a005150 = foldl1 (\v d -> 10 * v + d) . map toInteger . a034002_row
-- Reinhard Zumkeller, Aug 09 2012

Java
```
See Paulo Ortolan link.
```

RunLengthEncode[ x_List ] := (Through[ {First, Length}[ #1 ] ] &) /@ Split[ x ]; LookAndSay[ n_, d_:1 ] := NestList[ Flatten[ Reverse /@ RunLengthEncode[ # ] ] &, {d}, n - 1 ]; F[ n_ ] := LookAndSay[ n, 1 ][ [ n ] ]; Table[ FromDigits[ F[ n ] ], {n, 1, 15} ]
A005150[1] := 1; A005150[n_] := A005150[n] = FromDigits[Flatten[{Length[#], First[#]}&/@Split[IntegerDigits[A005150[n-1]]]]]; Map[A005150, Range[25]] (* Peter J. C. Moses, Mar 21 2013 *)

A005150(n,a=1)={ while(n--, my(c=1); for(j=2,#a=Vec(Str(a)), if( a[j-1]==a[j], a[j-1]=""; c++, a[j-1]=Str(c,a[j-1]); c=1)); a[#a]=Str(c,a[#a]); a=concat(a)); a }  \\ M. F. Hasler, Jun 30 2011

$str="1"; for (1 .. shift(@ARGV)) { print($str, ","); @a = split(//,$str); $str=""; $nd=shift(@a); while (defined($nd)) { $d=$nd; $cnt=0; while (defined($nd) && ($nd eq $d)) { $cnt++; $nd = shift(@a); } $str .= $cnt.$d; } } print($str);
# Jeff Quilici (jeff(AT)quilici.com), Aug 12 2003

# This outputs the first n elements of the sequence, where n is given on the command line.
$s = 1;
for (2..shift @ARGV) {
print "$s, ";
$s =~ s/(.)\1*/(length $&).$1/eg;
}
# Arne 'Timwi' Heizmann (timwi(AT)gmx.net), Mar 12 2008
print "$s\n";

def A005150(n):
    p = "1"
    seq = [1]
    while (n > 1):
        q = ''
        idx = 0 # Index
        l = len(p) # Length
        while idx < l:
            start = idx
            idx = idx + 1
            while idx < l and p[idx] == p[start]:
                idx = idx + 1
            q = q + str(idx-start) + p[start]
        n, p = n - 1, q
        seq.append(int(p))
    return seq
# Olivier Mengue (dolmen(AT)users.sourceforge.net), Jul 01 2005

def A005150(n):
    seq = [1] + [None] * (n - 1) # allocate entire array space
    def say(s):
        acc = '' # initialize accumulator
        while len(s) > 0:
            i = 0
            c = s[0] # char of first run
            while (i < len(s) and s[i] == c): # scan first digit run
                i += 1
            acc += str(i) + c # append description of first run
            if i == len(s):
                break # done
            else:
                s = s[i:] # trim leading run of digits
        return acc
    for i in range(1, n):
        seq[i] = int(say(str(seq[i-1])))
    return seq
# E. Johnson (ejohnso9(AT)earthlink.net), Mar 31 2008

# program without string operations
def sign(n): return int(n > 0)
def say(a):
    r = 0
    p = 0
    while a > 0:
        c = 3 - sign((a % 100) % 11) - sign((a % 1000) % 111)
        r += (10 * c + (a % 10)) * 10**(2*p)
        a //= 10**c
        p += 1
    return r
a = 1
for i in range(1, 26):
    print(i, a)
    a = say(a)
# Volker Diels-Grabsch, Aug 18 2013

import re
def lookandsay(limit, sequence = 1):
    if limit > 1:
        return lookandsay(limit-1, "".join([str(len(match.group()))+match.group()[0] for matchNum, match in enumerate(re.finditer(r"(\w)\1*", str(sequence)))]))
    else:
        return sequence
# lookandsay(3) --> 21
# Nicola Vanoni, Nov 29 2016

import itertools
x = "1"
for i in range(20):
    print(x)
    x = ''.join(str(len(list(g)))+k for k,g in itertools.groupby(x))
# Matthew Cotton, Nov 12 2019

a(n+1) = A045918(a(n)). - Reinhard Zumkeller, Aug 09 2012
a(n) = Sum_{k=1..A005341(n)} A034002(n,k)*10^(A005341(n)-k). - Reinhard Zumkeller, Dec 15 2012
a(n) = A004086(A007651(n)). - Bernard Schott, Jan 08 2021
A055642(a(n+1)) = A005341(n+1) = 2*A043562(a(n)). - Ya-Ping Lu, Jan 28 2025
Conjecture: DC(a(n)) ~ k * (Conway's constant)^n where k is approximately 1.021... and DC denotes the number of digit changes in the decimal representation of n (e.g., DC(13112221)=4 because 1->3, 3-1, 1->2, 2->1). - Bill McEachen, May 09 2025
Conjecture: lim_{n->infinity} (c2+c3-c1)/(c1+c2+c3) = 0.01 approximately, where ci is the number of appearances of 'i' in a(n). - Ya-Ping Lu, Jun 05 2025

A006715 Describe the previous term! (method A - initial term is 3).

Original entry on oeis.org

3, 13, 1113, 3113, 132113, 1113122113, 311311222113, 13211321322113, 1113122113121113222113, 31131122211311123113322113, 132113213221133112132123222113, 11131221131211132221232112111312111213322113, 31131122211311123113321112131221123113111231121123222113

Offset: 1

N. J. A. Sloane

Method A = 'frequency' followed by 'digit'-indication.

a(n+1) - a(n) is divisible by 10^5 for n > 5. - Altug Alkan, Dec 04 2015

			The term after 3113 is obtained by saying "one 3, two 1's, one 3", which gives 132113.

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
Éric Brier, Rémi Géraud-Stewart, David Naccache, Alessandro Pacco, and Emanuele Troiani, Stuttering Conway Sequences Are Still Conway Sequences, arXiv:2006.06837 [math.DS], 2020.
Éric Brier, Rémi Géraud-Stewart, David Naccache, Alessandro Pacco, and Emanuele Troiani, The Look-and-Say The Biggest Sequence Eventually Cycles, arXiv:2006.07246 [math.DS], 2020.
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.

Cf. A001140, A001141, A001143, A001145, A001151, A001154, A001155, A005150, A006751.

Cf. A088204 (continuous version).

RunLengthEncode[ x_List ] := (Through[ {First, Length}[ #1 ] ] &) /@ Split[ x ]; LookAndSay[ n_, d_:1 ] := NestList[ Flatten[ Reverse /@ RunLengthEncode[ # ] ] &, {d}, n - 1 ]; F[ n_ ] := LookAndSay[ n, 3 ][ [ n ] ]; Table[ FromDigits[ F[ n ] ], {n, 11} ] (* Zerinvary Lajos, Mar 21 2007 *)

# This outputs the first n elements of the sequence, where n is given on the command line.
$s = 3;
for (2..shift @ARGV) {
    print "$s, ";
    $s =~ s/(.)\1*/(length $&).$1/eg;
}
print "$s\n";
## Arne 'Timwi' Heizmann (timwi(AT)gmx.net), Mar 12 2008

A001155 Describe the previous term! (method A - initial term is 0).

Original entry on oeis.org

0, 10, 1110, 3110, 132110, 1113122110, 311311222110, 13211321322110, 1113122113121113222110, 31131122211311123113322110, 132113213221133112132123222110, 11131221131211132221232112111312111213322110, 31131122211311123113321112131221123113111231121123222110

Offset: 1

N. J. A. Sloane

Method A = 'frequency' followed by 'digit'-indication.
a(n), A001140, A001141, A001143, A001145, A001151 and A001154 are all identical apart from the last digit of each term (the seed). This is because digits other than 1, 2 and 3 never arise elsewhere in the terms (other than at the end of each of them) of look-and-say sequences of this type (as is mentioned by Carmine Suriano in A006751). - Chayim Lowen, Jul 16 2015
a(n+1) - a(n) is divisible by 10^5 for n > 5. - Altug Alkan, Dec 04 2015

			The term after 3110 is obtained by saying "one 3, two 1's, one 0", which gives 132110.

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.
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]

Cf. A005150, A006751, A006715, A001140, A001141, A001143, A001145, A001151, A001154.

Cf. A036058.

A001155[1] := 0; A001155[n_] := A001155[n] = FromDigits[Flatten[{Length[#], First[#]}&/@Split[IntegerDigits[A001155[n-1]]]]]; Map[A001155,Range[15]] (* Peter J. C. Moses, Mar 21 2013 *)

A001155(n,a=0)={ while(n--, my(c=1); for(j=2,#a=Vec(Str(a)), if( a[j-1]==a[j], a[j-1]=""; c++, a[j-1]=Str(c,a[j-1]); c=1)); a[#a]=Str(c,a[#a]); a=concat(a)); a }  \\ M. F. Hasler, Jun 30 2011

from itertools import accumulate, groupby, repeat
def summarize(n, _): return int("".join(str(len(list(g)))+k for k, g in groupby(str(n))))
def aupton(terms): return list(accumulate(repeat(0, terms), summarize))
print(aupton(11)) # Michael S. Branicky, Jun 28 2022

A001151 Describe the previous term! (method A - initial term is 8).

Original entry on oeis.org

8, 18, 1118, 3118, 132118, 1113122118, 311311222118, 13211321322118, 1113122113121113222118, 31131122211311123113322118, 132113213221133112132123222118, 11131221131211132221232112111312111213322118, 31131122211311123113321112131221123113111231121123222118

Offset: 1

N. J. A. Sloane

Method A = 'frequency' followed by 'digit'-indication.

a(n+1) - a(n) is divisible by 10^5 for n > 5. - Altug Alkan, Dec 04 2015

			E.g. the term after 3118 is obtained by saying "one 3, two 1's, one 8", which gives 132118.

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.
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]

Cf. A001155, A005150, A006751, A006715, A001140, A001141, A001143, A001145, A001154.

freq := proc(i,L)
    local f,p ;
    if i > nops(L) or i < 1 then
        return 0 ;
    end if;
    f := 1 ;
    for p from i to 2 by -1 do
        if op(p,L) = op(p-1,L) then
            f := f+1 ;
        else
            return f;
        end if;
    end do:
    f ;
end proc:
read("transforms"):
rle := proc(n)
    local inL,i,outL,f ;
    inL := convert(n,base,10) ;
    i := nops(inL) ;
    outL := [] ;
    while i>0 do
        f := freq(i,inL) ;
        if f = 0 then
            break;
        else
            outL := [op(outL),f,op(i,inL)] ;
            i := i-f ;
        end if;
    end do:
    digcatL(outL) ;
end proc:
A001151 := proc(n)
    option remember ;
    if n = 1 then
        8;
    else
        rle(procname(n-1)) ;
    end if;
end proc:
seq(A001151(n),n=1..10) ; # R. J. Mathar, Feb 11 2021

RunLengthEncode[x_List] := (Through[{First, Length}[ #1]] &) /@ Split[x]; LookAndSay[n_, d_: 1] := NestList[Flatten[Reverse /@ RunLengthEncode[ # ]] &, {d}, n - 1]; F[n_] := LookAndSay[n, 8][[n]]; Table[FromDigits[F[n]], {n, 1, 11}] (* Zerinvary Lajos, Jul 08 2009 *)

A225224 A continuous "look-and-say" sequence (without repetition, seed 1,1,1).

Original entry on oeis.org

1, 1, 1, 3, 1, 1, 3, 2, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 2, 1, 3, 2, 2, 1, 1, 3, 1, 2, 1, 1, 1, 3, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 3, 1, 1, 3, 3, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 3, 2, 1, 2, 3, 2, 2, 2, 1, 2, 3, 2, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1

Offset: 1

Jean-Christophe Hervé, May 02 2013

A variant of the Conway's 'look-and-say' sequence A005150, without run cut-off. It describes at each step the preceding numbers taken altogether.
The sequence is better described as starting with three 1's: 1, 1, 1, and then 3, 1, and 1, 3, etc., as seed one creates a singular case: 1, then 1, 1, which can be continued either as 2, 1 (ignoring the aforesaid first 1, cf. A221646), or as 3, 1, considering twice the first one.
Contrary to the original look-and-say, this sequence is not base dependent, because figures or group of figures are not aggregated and read as numbers.
The sequence is determined by pairs. Terms of even ranks are counts while odd ranks are numbers.
As in the original look-and-say sequence, a(n) is always equal to 1, 2 or 3. The subsequence 3,3,3 never appears.
Two successive odd ranks cannot be equal, which implies that sequences of length three always begin on even rank and that two such sequences never follow each other.
Applying the look-and-say principle to the sequence itself, it is simply shift three ranks to the left.
With seed 2 (resp. 3), the sequence is A088203 (resp. A088204). These two sequences are shifted one rank left by the look-and-say transform.
With seed 2, the sequence A088203 is the concatenation of A006751 (original look-and-say method by blocks): this is because all blocks begin with 1 or 3 and end with 2 and therefore, there is no possible interaction between blocks after concatenation.

			The sequence starts with: 1, 1, 1
The first group has three 1's: 3, 1
The next group has one 3: 1, 3
The next group has two 1's: 2, 1
The next group has one 3: 1, 3
The next group has one 2: 1, 2
The next group has two 1's: 2, 1, etc.

J.-C. Hervé, Table of n, a(n) for n = 1..10000

Cf. A005150 (original look-and-say sequence).
Cf. A221646 (a close variant with seed 1).
Cf. A225212 (a variant with nested repetitions).
Cf. A088203 (seed 2), A088204 (seed 3).
Cf. A225330 (look-and-repeat).

/* computes first n terms in array a[] */
int *swys(int n) {
int a[n] ;
int see, say, c ;
a[0] = 1;
see = say = 0 ;
while( say < n-1 ) {
  c = 0 ;     /* count */
  dg = a[see] /* digit */
  if (say > 0) { /* not the first time */
    while (see <= say) {
      if (a[see]== dg)  c += 1 ;
      else break ;
      see += 1 ;
      }
    }
  else {
   c = 1 ;
    }
  a[++say] = c ;
  if (say < n-1) a[++say] = dg ;
  }
return(a);
}

n = 100; a[0] = 1; see = say = 0; While[ say < n - 1, c = 0; dg = a[see]; If[say > 0, While[ see <= say, If[a[see] == dg, c += 1, Break[]]; see += 1], c = 1]; a[++say] = c; If[say < n - 1, a[++say] = dg]]; Array[a, n, 0] (* Jean-François Alcover, Jul 11 2013, translated and adapted from J.-C. Hervé's C program *)

A001140 Describe the previous term! (method A - initial term is 4).

Original entry on oeis.org

4, 14, 1114, 3114, 132114, 1113122114, 311311222114, 13211321322114, 1113122113121113222114, 31131122211311123113322114, 132113213221133112132123222114, 11131221131211132221232112111312111213322114, 31131122211311123113321112131221123113111231121123222114

Offset: 1

N. J. A. Sloane

Method A = 'frequency' followed by 'digit'-indication.
A001155, A001140, A001141, A001143, A001145, A001151 and A001154 are all identical apart from the last digit of each term (the seed). This is because digits other than 1, 2 and 3 never arise elsewhere in the terms (other than at the end of each of them) of look-and-say sequences of this type (as is mentioned by Carmine Suriano in A006751). - Chayim Lowen, Jul 16 2015
a(n+1) - a(n) is divisible by 10^5 for n > 5. - Altug Alkan, Dec 04 2015

			The term after 3114 is obtained by saying "one 3, two 1's, one 4", which gives 132114.

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.
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]

Cf. A001155, A005150, A006751, A006715, A001141, A001143, A001145, A001151, A001154.

cf. Josh Triplett's program for A005051.
import Data.List (group)
a001140 n = a001140_list !! (n-1)
a001140_list = 4 : map say a001140_list where
   say = read . concatMap saygroup . group . show
         where saygroup s = (show $ length s) ++ [head s]
-- Reinhard Zumkeller, Dec 15 2012

RunLengthEncode[ x_List ] := (Through[ {First, Length}[ #1 ] ] &) /@ Split[ x ];
LookAndSay[ n_, d_:1 ] := NestList[ Flatten[ Reverse /@ RunLengthEncode[ # ] ] &, {d}, n - 1 ];
F[ n_ ] := LookAndSay[ n, 4 ][ [ n ] ];
Table[ FromDigits[ F[ n ] ], {n, 1, 11} ] (* Zerinvary Lajos, Mar 21 2007 *)

# This outputs the first n elements of the sequence, where n is given on the command line.
$s = 4;
for (2..shift @ARGV) {
    print "$s, ";
    $s =~ s/(.)\1*/(length $&).$1/eg;
}
print "$s\n";
## Arne 'Timwi' Heizmann (timwi(AT)gmx.net), Mar 12 2008

cp's OEIS Frontend

A265849 First differences of A006751.

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A005150 Look and Say sequence: describe the previous term! (method A - initial term is 1).

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A006715 Describe the previous term! (method A - initial term is 3).

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A001155 Describe the previous term! (method A - initial term is 0).

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A001151 Describe the previous term! (method A - initial term is 8).

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A225224 A continuous "look-and-say" sequence (without repetition, seed 1,1,1).

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