A023989 -id:A023989 - cp's OEIS frontend

A005151 Summarize the previous term (digits in increasing order), starting with a(1) = 1.

1, 11, 21, 1112, 3112, 211213, 312213, 212223, 114213, 31121314, 41122314, 31221324, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314

Offset: 1

N. J. A. Sloane

a(n) = 21322314 for n > 12. - Reinhard Zumkeller, Jan 25 2014

The digits of each term a(n) are a permutation of those of the corresponding term A063850(n). - Chayim Lowen, Jul 16 2015

			The term after 312213 is obtained by saying "Two 1's, two 2's, two 3's", which gives 21-22-23, i.e., 212223.

C. Fleenor, "A litteral sequence", Solution to Problem 2562, Journal of Recreational Mathematics, vol. 31 No. 4 pp. 307 2002-3 Baywood NY.
Problem in J. Recreational Math., 30 (4) (1999-2000), p. 309.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Colin Barker, Table of n, a(n) for n = 1..1000
V. Bronstein and A. S. Fraenkel, On a curious property of counting sequences, Amer. Math. Monthly, 101 (1994), 560-563.
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.
X. Gourdon and B. Salvy, Effective asymptotics of linear recurrences with rational coefficients, Discrete Mathematics, vol. 153, no. 1-3, 1996, pages 145-163.
James Henle, Is (some) mathematics poetry?, Journal of Humanistic Mathematics 1:1 (2011), pp. 94-100.
Madras Math's Amazing Number Facts, Fact No. 13
Madras Math, Descriptive Number
Trevor Scheopner, The Cyclic Nature (and Other Intriguing Properties) of Descriptive Numbers, Princeton Undergraduate Mathematics Journal, Issue 1, Article 4.
L. J. Upton, Letter to N. J. A. Sloane, Jan 8 1991.
Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A005150, A047842. See A083671 for another version.

Cf. A023989, A118628, A060857.

import Data.List (group, sort, transpose)
a005151 n = a005151_list !! (n-1)
a005151_list = 1 : f [1] :: [Integer] where
   f xs = (read $ concatMap show ys) : f ys where
          ys = concat $ transpose [map length zss, map head zss]
          zss = group $ sort xs
-- Reinhard Zumkeller, Jan 25 2014

RunLengthEncode[x_List] := (Through[{Length, First}[ #1]] &) /@ Split[ Sort[x]]; LookAndSay[n_, d_:1] := NestList[ Flatten[ RunLengthEncode[ # ]] &, {d}, n - 1]; F[n_] := LookAndSay[n, 1][[n]]; Table[ FromDigits[ F[n]], {n, 25}] (* Robert G. Wilson v, Jan 22 2004 *)
a[1] = 1; a[n_] := a[n] = FromDigits[Reverse /@ Sort[Tally[a[n-1] // IntegerDigits], #1[[1]] < #2[[1]]&] // Flatten]; Array[a, 26] (* Jean-François Alcover, Jan 25 2016 *)

say(n) = {digs = digits(n); d = vecsort(digs,,8); s = ""; for (k=1, #d, nbk = #select(x->x==d[k], digs); s = concat(s, Str(nbk)); s = concat(s, d[k]);); eval(s);}
lista(nn) = {print1(n = 1, ", "); for (k=1, nn, m = say(n); print1(m, ", "); n = m;);} \\ Michel Marcus, Feb 12 2016

a(n,show_all=1,a=1)={for(i=2,n,show_all&&print1(a",");a=A047842(a));a} \\ M. F. Hasler, Feb 25 2018

Vec(x*(1 + 10*x + 10*x^2 + 1091*x^3 + 2000*x^4 + 208101*x^5 + 101000*x^6 - 99990*x^7 - 98010*x^8 + 31007101*x^9 + 10001000*x^10 - 9900990*x^11 - 9899010*x^12) / (1 - x) + O(x^40)) \\ Colin Barker, Aug 23 2018

from itertools import accumulate, groupby, repeat
def summarize(n, _):
  return int("".join(str(len(list(g)))+k for k, g in groupby(sorted(str(n)))))
def aupton(nn): return list(accumulate(repeat(1, nn+1), summarize))
print(aupton(25)) # Michael S. Branicky, Jan 11 2021

a(n+1) = A047842(a(n)). - M. F. Hasler, Feb 25 2018

G.f.: x*(1 + 10*x + 10*x^2 + 1091*x^3 + 2000*x^4 + 208101*x^5 + 101000*x^6 - 99990*x^7 - 98010*x^8 + 31007101*x^9 + 10001000*x^10 - 9900990*x^11 - 9899010*x^12) / (1 - x). - Colin Barker, Aug 23 2018

A118628 "Say what you see".

Original entry on oeis.org

3, 13, 1113, 3113, 2123, 112213, 312213, 212223, 114213, 31121314, 41122314, 31221324, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314

Offset: 1

Parthasarathy Nambi, May 09 2006

nonn

			3 = "one three" --> 13
13 = "one one, one three" --> 1113
1113 = "three ones, one three" --> 3113
3113 = "two ones, two threes" --> 2123

Madras College, Descriptive Numbers

Cf. A005151.

Cf. A047842, A023989.

import Data.List (group, sort, transpose)
a118628 n = a118628_list !! (n-1)
a118628_list = 3 : f [3] :: [Integer] where
   f xs = (read $ concatMap show ys) : f (ys) where
          ys = concat $ transpose [map length zss, map head zss]
          zss = group $ sort xs
-- Reinhard Zumkeller, Jan 26 2014

a(n) = 21322314 for n > 12; a(n) = A005151(n) for n > 6. - Reinhard Zumkeller, Jan 26 2014

a(n) = A047842(a(n-1)). - Pontus von Brömssen, Jun 04 2023

A121993 Numbers k that yield a smaller number a(k) under the "Look and Say" function A045918.

Original entry on oeis.org

33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 1222, 1333, 1444, 1555, 1666, 1777, 1888, 1999, 2000, 2111, 2222, 2233, 2244, 2255, 2266, 2277, 2288, 2299, 2333, 2444, 2555, 2666, 2777, 2888, 2999, 3000, 3111, 3222, 3300, 3311

Offset: 1

Sergio Pimentel, Sep 11 2006

			a(26)=2000 because under the Look and Say operator, 2000 is described as one two three zeros or: 1230, which is smaller than 2000.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Look and Say Sequence.

Cf. A045918, A005150, A005341, A023989, A079475.

a121993 n = a121993_list !! (n-1)
a121993_list = filter (\x -> a045918 x < x) [0..]
-- Reinhard Zumkeller, Jan 25 2014

from itertools import groupby
def ok(n): return n > int(''.join(str(len(list(g)))+k for k, g in groupby(str(n))))
print([k for k in range(3312) if ok(k)]) # Michael S. Branicky, May 26 2023

A037192 Summarize the previous term!, starting with 8899.

Original entry on oeis.org

8899, 2829, 221819, 21221819, 31321819, 3112231819, 4122231819, 313213141819, 511233141819, 51122314151819, 61221314251819, 5132131415161819, 7112231425161819, 613213141516171819, 811223141526171819

Offset: 0

Dave Ellis (djellis(AT)hotmail.com)

Cf. A005151, A023989, A037220.

More terms from Erich Friedman.

A121994 Smallest natural number that yields a sequence of n decreasing numbers under the "Look and Say" operator A045918.

Original entry on oeis.org

1, 33, 333, 333111, 33333333333333333333333333333333311111111111

Offset: 0

Sergio Pimentel, Sep 11 2006

a(5) <= 33333333333333333333333333333333 '3's concatenated with 1111111111 '1's. - Tyler Busby, Feb 07 2023

			a(3)=333111 because under the Look and Say operator sequence A045918 it yields: 3331, 3311, 2321 which are all decreasing (3 in a row). The next term would be 12131211 which is greater than 2321.

Eric Weisstein's World of Mathematics, Look and Say.

Cf. A045918, A005150, A005341, A023989, A079475.

a(4) from Sergio Pimentel, Mar 05 2008

a(4) corrected by Tyler Busby, Feb 07 2023

cp's OEIS Frontend

A005151 Summarize the previous term (digits in increasing order), starting with a(1) = 1.

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A118628 "Say what you see".

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A121993 Numbers k that yield a smaller number a(k) under the "Look and Say" function A045918.

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A037192 Summarize the previous term!, starting with 8899.

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A121994 Smallest natural number that yields a sequence of n decreasing numbers under the "Look and Say" operator A045918.

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