A022513 -id:A022513 - cp's OEIS frontend

A006711 Describe previous term from the right (method A - initial term is 1).

1, 11, 21, 1112, 1231, 11131211, 2112111331, 112331122112, 12212221231221, 11221113121132112211, 212221121321121113312221, 113211233112211213111221321112

Offset: 1

N. J. A. Sloane

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

			E.g. the term after 1231 is obtained by saying "one 1, one 3, one 2, one 1", which gives 11131211.

J. H. Conway, personal communication.
Akhlesh Lakhtakia and C. A. Pickover, Observations on the Gleichniszahlen-Reihe: An Unusual Number Theory Sequence, J. Rec. Math., Vol. 25 #3, pp. 189-192, 1993.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Reinhard Zumkeller, Table of n, a(n) for n = 1..24
Onno M. Cain, Sela T. Enin, Inventory Loops (i.e. Counting Sequences) have Pre-period 2 max S_1 + 60, arXiv:2004.00209 [math.NT], 2020.
Trevor Scheopner, The Cyclic Nature (and Other Intriguing Properties) of Descriptive Numbers, Princeton Undergraduate Mathematics Journal, Issue 1, Article 4.
Eric Weisstein's World of Mathematics, Look and Say Sequence
Wikipedia, Look-and-say sequence

Cf. A005150, A022506, A022482, A022507-A022513.

a006711 n = a006711_list !! (n-1)
a006711_list = iterate (a045918 . a004086) 1
-- Reinhard Zumkeller, Mar 02 2014

A006711[1]:=1;A006711[n_]:=A006711[n]=FromDigits[Flatten[{Length[#],First[#]}&/@Split[Reverse[IntegerDigits[A006711[n-1]]]]]];Map[A006711,Range[15]] (* Peter J. C. Moses, Apr 22 2013 *)

a(n+1) = A045918(A004086(a(n))). - Reinhard Zumkeller, Mar 02 2014

A022482 Describe previous term from the right (method A - initial term is 2).

Original entry on oeis.org

2, 12, 1211, 211211, 21122112, 1221222112, 122132112211, 2122211213112211, 21222113111221321112, 123112131122311321321112, 123112131112132113222113111221131211

Offset: 1

Clark Kimberling

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

			E.g. the term after 1211 is obtained by saying "two 1's, one 2, one 1", which gives 211211.

Reinhard Zumkeller, Table of n, a(n) for n = 1..22
Eric Weisstein's World of Mathematics, Look and Say Sequence
Wikipedia, Look-and-say sequence

Cf. A022506, A006711, A022507-A022513.

a022482 n = a022482_list !! (n-1)
a022482_list = iterate (a045918 . a004086) 2
-- Reinhard Zumkeller, Mar 02 2014

A022482[1]:=2;A022482[n_]:=A022482[n]=FromDigits[Flatten[{Length[#],First[#]}&/@Split[Reverse[IntegerDigits[A022482[n-1]]]]]];Map[A022482,Range[15]] (* Peter J. C. Moses, Apr 22 2013 *)

a(n+1) = A045918(A004086(a(n))). - Reinhard Zumkeller, Mar 02 2014

A022506 Describe previous term from the right (method A - initial term is 0).

Original entry on oeis.org

0, 10, 1011, 211011, 21102112, 122112102112, 122112101112212211, 2122112231101112212211, 21221122311021132221221112, 12312211321321121021132221221112

Offset: 0

N. J. A. Sloane

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

			The term after 1011 is obtained by saying "two 1's, one 0, one 1", which gives 211011.

Reinhard Zumkeller, Table of n, a(n) for n = 0..21
Eric Weisstein's World of Mathematics, Look and Say Sequence
Wikipedia, Look-and-say sequence

Cf. A006711, A022482, A022507-A022513.

a022506 n = a022506_list !! n
a022506_list = 0 : 10 : iterate (a045918 . a004086) 1011
-- Reinhard Zumkeller, Mar 02 2014

a[0] = 0;
a[n_] := a[n] = Split[IntegerDigits[a[n-1]]] /. L_List /; IntegerQ[L[[1]]] :> {Length[L], L[[1]]} // Reverse // Flatten // FromDigits;
a /@ Range[0, 9] (* Jean-François Alcover, Nov 26 2019 *)

For n > 1: a(n+1) = A045918(A004086(a(n))). - Reinhard Zumkeller, Mar 02 2014

More terms from Erich Friedman

A022507 Describe previous term from the right (method A - initial term is 3).

Original entry on oeis.org

3, 13, 1311, 211311, 21132112, 122112132112, 122112131112212211, 2122112231131112212211, 21221122311321132221221112, 12312211321321121321132221221112

Offset: 0

N. J. A. Sloane

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

			The term after 1311 is obtained by saying "two 1's, one 3, one 1", which gives 211311.

Reinhard Zumkeller, Table of n, a(n) for n = 0..21
Eric Weisstein's World of Mathematics, Look and Say Sequence
Wikipedia, Look-and-say sequence

Cf. A022506, A006711, A022482, A022508-A022513.

a022507 n = a022507_list !! n
a022507_list = iterate (a045918 . a004086) 3
-- Reinhard Zumkeller, Mar 02 2014

A022507[1]:=3;A022507[n_]:=A022507[n]=FromDigits[Flatten[{Length[#],First[#]}&/@Split[Reverse[IntegerDigits[A022507[n-1]]]]]];Map[A022507,Range[15]] (* Peter J. C. Moses, Apr 22 2013 *)

a(n+1) = A045918(A004086(a(n))). - Reinhard Zumkeller, Mar 02 2014

More terms from Erich Friedman

A138484 Say what you see in previous term, from the right, reporting total number for each digit encountered. Initial term is 0.

Original entry on oeis.org

0, 10, 1011, 3110, 102113, 13311210, 10411223, 1322311410, 1041142322, 3213243110, 1031331422, 2214313310, 1031331422, 2214313310, 1031331422, 2214313310, 1031331422, 2214313310, 1031331422, 2214313310, 1031331422

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, Mar 20 2008

After a while sequence has period 2 -> {1031331422,2214313310}

			To get the term after 102113, we say: one 3's, three 1's, one 2's, one 0's, so 13311210.

Cf. A063850, A022482, A005150, A005151, A006751, A006715, A006711, A022506-A022513, A138485-A138493.

A138493 Say what you see in previous term, from the right, reporting total number for each digit encountered. Initial term is 9.

Original entry on oeis.org

9, 19, 1911, 3119, 192113, 13311219, 19411223, 1322311419, 1941142322, 3213243119, 1931331422, 2214313319, 1931331422, 2214313319, 1931331422, 2214313319, 1931331422, 2214313319, 1931331422, 2214313319, 1931331422

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, Mar 20 2008

After a while sequence has period 2 -> {1931331422,2214313319}

			To get the term after 192113, we say: one 3's, three 1's, one 2's, one 9's, so 13311219

Cf. A063850, A022482, A005150, A005151, A006751, A006715, A006711, A022506-A022513, A138484-A138492.

A022508 Describe previous term from the right (method A - initial term is 4).

Original entry on oeis.org

4, 14, 1411, 211411, 21142112, 122112142112, 122112141112212211, 2122112231141112212211, 21221122311421132221221112, 12312211321321121421132221221112

Offset: 0

N. J. A. Sloane

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

			The term after 1411 is obtained by saying "two 1's, one 4, one 1", which gives 211411.

Cf. A022506, A006711, A022482, A022507-A022513.

A022508[1]:=4;A022508[n_]:=A022508[n]=FromDigits[Flatten[{Length[#],First[#]}&/@Split[Reverse[IntegerDigits[A022508[n-1]]]]]];Map[A022508,Range[15]] (* Peter J. C. Moses, Apr 22 2013 *)

More terms from Erich Friedman

A022511 Describe previous term from the right (method A - initial term is 7).

Original entry on oeis.org

7, 17, 1711, 211711, 21172112, 122112172112, 122112171112212211, 2122112231171112212211, 21221122311721132221221112, 12312211321321121721132221221112

Offset: 0

N. J. A. Sloane

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

			The term after 1711 is obtained by saying "two 1's, one 7, one 1", which gives 211711.

Michael De Vlieger, Table of n, a(n) for n = 0..21

Cf. A022506, A006711, A022482, A022507-A022513.

NestList[FromDigits@ Flatten@ Map[Reverse@ Flatten@ Tally[#] &, Split@ Reverse@ IntegerDigits[#]] &, 7, 9] (* Michael De Vlieger, Dec 16 2021 *)

More terms from Erich Friedman

A022512 Describe previous term from the right (method A - initial term is 8).

Original entry on oeis.org

8, 18, 1811, 211811, 21182112, 122112182112, 122112181112212211, 2122112231181112212211, 21221122311821132221221112, 12312211321321121821132221221112

Offset: 0

N. J. A. Sloane

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

			E.g., the term after 1811 is obtained by saying "two 1's, one 8, one 1", which gives 211811.

Cf. A022506, A006711, A022482, A022507-A022513.

split[n_]:=Split[Reverse[IntegerDigits[n]]];
list1[n_]:=List/@Length/@split[n];riffle1[n_]:=Riffle[split[n],list1[n]];
tab[n_]:=Table[i,{i,1,2*Length[list1[n]],2}];
list2[n_]:=Append[riffle1[n][[#]],riffle1[n][[#+1]]]&/@tab[n];
flat[n_]:=Flatten/@list2[n];riffle2[n_]:=Riffle[Last/@flat[n],First/@flat[n]];
a[1]=8; a[n_]:=FromDigits[riffle2[a[n-1]]]; Array[a,10] (* or *)
IntegerReverse[NestList[FromDigits[Flatten[Replace[Replace[Replace[Split[Reverse[IntegerDigits[#]]],{x_,y_}->{x,Length[{x,y}]},{1}],{x_,y_,z_}->{x,Length[{x,y,z}]},{1}],{x_}->{x,Length[{x}]},{1}]]]&,8,9]] (* Ivan N. Ianakiev, Nov 10 2016 *)

More terms from Erich Friedman

A138485 Say what you see in previous term, from the right, reporting total number for each digit encountered. Initial term is 1.

Original entry on oeis.org

1, 11, 21, 1112, 1231, 211312, 223113, 232122, 421113, 13311214, 14411223, 13223124, 14322123, 23322114, 14213223, 23322114, 14213223, 23322114, 14213223, 23322114, 14213223, 23322114, 14213223, 23322114, 14213223

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, Mar 20 2008

After a while sequence has period 2 -> {23322114,14213223}

			To get the term after 211312, we say: two 2's, three 1's, one 3's, so 223113.

Cf. A063850, A022482, A005150, A005151, A006751, A006715, A006711, A022506-A022513, A138484, A138486-A138493.

cp's OEIS Frontend

A006711 Describe previous term from the right (method A - initial term is 1).

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A022482 Describe previous term from the right (method A - initial term is 2).

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A022506 Describe previous term from the right (method A - initial term is 0).

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A022507 Describe previous term from the right (method A - initial term is 3).

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A138484 Say what you see in previous term, from the right, reporting total number for each digit encountered. Initial term is 0.

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A138493 Say what you see in previous term, from the right, reporting total number for each digit encountered. Initial term is 9.

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A022508 Describe previous term from the right (method A - initial term is 4).

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A022511 Describe previous term from the right (method A - initial term is 7).

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