A006711
Describe previous term from the right (method A - initial term is 1).
Original entry on oeis.org
1, 11, 21, 1112, 1231, 11131211, 2112111331, 112331122112, 12212221231221, 11221113121132112211, 212221121321121113312221, 113211233112211213111221321112
Offset: 1
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
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
E.g. the term after 1211 is obtained by saying "two 1's, one 2, one 1", which gives 211211.
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
The term after 1011 is obtained by saying "two 1's, one 0, one 1", which gives 211011.
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a022506 n = a022506_list !! n
a022506_list = 0 : 10 : iterate (a045918 . a004086) 1011
-- Reinhard Zumkeller, Mar 02 2014
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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 *)
A022513
Describe previous term from the right (method A - initial term is 9).
Original entry on oeis.org
9, 19, 1911, 211911, 21192112, 122112192112, 122112191112212211, 2122112231191112212211, 21221122311921132221221112, 12312211321321121921132221221112
Offset: 0
E.g., the term after 1911 is obtained by saying "two 1's, one 9, one 1", which gives 211911.
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
The term after 1411 is obtained by saying "two 1's, one 4, one 1", which gives 211411.
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
The term after 1711 is obtained by saying "two 1's, one 7, one 1", which gives 211711.
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NestList[FromDigits@ Flatten@ Map[Reverse@ Flatten@ Tally[#] &, Split@ Reverse@ IntegerDigits[#]] &, 7, 9] (* Michael De Vlieger, Dec 16 2021 *)
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
E.g., the term after 1811 is obtained by saying "two 1's, one 8, one 1", which gives 211811.
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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 *)
A022509
Describe previous term from the right (method A - initial term is 5).
Original entry on oeis.org
5, 15, 1511, 211511, 21152112, 122112152112, 122112151112212211, 2122112231151112212211, 21221122311521132221221112, 12312211321321121521132221221112
Offset: 0
The term after 1511 is obtained by saying "two 1's, one 5, one 1", which gives 211511.
A022510
Describe previous term from the right (method A - initial term is 6).
Original entry on oeis.org
6, 16, 1611, 211611, 21162112, 122112162112, 122112161112212211, 2122112231161112212211, 21221122311621132221221112, 12312211321321121621132221221112
Offset: 0
E.g., the term after 1611 is obtained by saying "two 1's, one 6, one 1", which gives 211611.
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a[1]=6; a[n_]:= a[n]= IntegerReverse[ FromDigits[ Flatten[ Replace[ Replace[ Replace[ Split[ IntegerDigits[a[n-1]]], {x_,y_}->{x,Length[{x,y}]},{1}], {x_,y_,z_}->{x,Length[{x,y,z}]},{1}], {x_}->{x,Length[{x}]},{1}]]]];
Array[a,10] (* Ivan N. Ianakiev, Jul 23 2019 *)
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from re import split
A022510_list, l = [6], '6'
for _ in range(10):
l = ''.join(str(len(d))+d[0] for d in split('(0+|1+|2+|3+|4+|5+|6+|7+|8+|9+)',l[::-1]) if d)
A022510_list.append(int(l)) # Chai Wah Wu, Jan 02 2015
Showing 1-9 of 9 results.
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