A005151 -id:A005151 - cp's OEIS frontend

A209233 A two-digit Look-and-Say sequence starting with 11: each term summarizes the increasing two-digit substrings of the previous term.

11, 111, 211, 111121, 311112121, 311212221131, 211212113221222231, 211312113421422123131132, 311212413114421122123331132134242, 411412313114421122123224331132233134141342144, 411312413414321322323124431232233234441242143244

Offset: 0

Reinhard Zumkeller, Jan 13 2013

a(16) is the first term containing a zero; this is due to the fact that a(15) is the first term having exactly 10 occurrences of a two-digit number, namely 10 x 31.

			a(0) = 11: 1 x 11 --> a(1) = 111;
a(1) = 111: 2 x 11 --> a(2) = 211;
a(2) = 211: 1 x 11 and 1 x 21 --> a(3) = 111121;
a(3) = 111121: 3 x 11, 1 x 12 and 1 x 21 --> a(4) = 311112121.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Look and Say Sequence
Wikipedia, Look-and-say sequence
Reinhard Zumkeller, Haskell program for two-digit Look-and-Say sequences

Cf. A005151, A047842.

Cf. A209234 (start=10), A221368 (start=12), A221369 (start=13), A221372 (start=19), A221373 (start=99).

Haskell
```
-- See Link.
```

A209234 A two-digit Look-and-Say sequence starting with 10: each term summarizes the increasing two-digit substrings of the previous term.

Original entry on oeis.org

10, 110, 110111, 101110311, 101103210311131, 101203310311113121231132, 101203210411312213120121123431132133, 201103104210311512413220421122123331232133134141143, 101203204310411412313214115220421222223124431232333134341242143151

Offset: 0

Reinhard Zumkeller, Jan 13 2013

			a(0) = 10: 1x10 --> a(1)=110;
a(1) = 110: 1x10 and 1x11 --> a(2)=110111;
a(2) = 110111: 1x01, 1x10 and 3x11 -> a(3)=101110311;
a(3) = 101110311: 1x01, 1x03, 2x10, 3x11 and 1x31 -> a(4)=101103210311131.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Look and Say Sequence
Wikipedia, Look-and-say sequence
Reinhard Zumkeller, Haskell program for two-digit Look-and-Say sequences

Cf. A005151, A047842, A001155.

Cf. A209233 (start=11), A221368 (start=12), A221369 (start=13), A221372 (start=19), A221373 (start=99).

Haskell
```
-- See Link.
```

A221368 A two-digit Look-and-Say sequence starting with 12: each term summarizes the increasing two-digit substrings of the previous term.

Original entry on oeis.org

12, 112, 111112, 411112, 311112141, 311112114121131141, 611212113214221231241, 211412113114421122123124131132141142161, 611412313414116621122123124331132341242144161, 411512213314216321122323224331132133234541142143144261162166

Offset: 0

Reinhard Zumkeller, Jan 13 2013

a(36) is the first term containing a zero; this is due to the fact that a(35) is the first term having exactly 10 occurrences of a two-digit number, namely 10 x 42.

			a(0) = 12: 1 x 12 --> a(1) = 112;
a(1) = 112: 1 x 11 ana 1 x 12 --> a(2) = 111112;
a(2) = 111112: 4 x 11 and 1 x 12 --> a(4) = 411112;
a(3) = 411112: 3 x 11, 1 x 12 and 1 x 41 --> a(4) = 311112141.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Look and Say Sequence
Wikipedia, Look-and-say sequence
Reinhard Zumkeller, Haskell program for two-digit Look-and-Say sequences

Cf. A005151, A047842.

Cf. A209234 (start=10), A209233 (start=11), A221369 (start=13), A221372 (start=19), A221373 (start=99).

Haskell
```
-- See Link.
```

A221372 A two-digit Look-and-Say sequence starting with 19: each term summarizes the increasing two-digit substrings of the previous term.

Original entry on oeis.org

19, 119, 111119, 411119, 311119141, 311114119131141191, 611113214219231241291, 311212113114119221123124129131132141142161191192, 911512313314116319521122123124129431132341142161291292

Offset: 0

Reinhard Zumkeller, Jan 13 2013

a(16) is the first term containing a zero; this is due to the fact that a(15) is the first term having exactly 10 occurrences of a two-digit number, namely 10 x 51.

			a(0) = 19: 1 x 19 --> a(1) = 119;
a(1) = 119: 1 x 11 and 1 x 19 --> a(2) = 111119;
a(2) = 111119: 4 x 11 and 1 x 19 --> a(3) = 411119;
a(3) = 411119: 3 x 11, 1 x 19 and 1 x 41 --> a(4) = 311119141.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Look and Say Sequence
Wikipedia, Look-and-say sequence
Reinhard Zumkeller, Haskell program for two-digit Look-and-Say sequences

Cf. A005151, A047842.

Cf. A209234 (start=10), A209233 (start=11), A221368 (start=12), A221369 (start=13), A221373 (start=99).

Haskell
```
-- See Link.
```

A221373 A two-digit Look-and-Say sequence starting with 99: each term summarizes the increasing two-digit substrings of the previous term.

Original entry on oeis.org

99, 199, 119199, 111219191199, 311112319121291199, 411312219121123129231291199, 311512113219221122223229331141291192199, 511312113114115319421522123229231232133141151191292193199, 611412313214315419521222323229631232133241142251152153191292193194199

Offset: 0

Reinhard Zumkeller, Jan 13 2013

a(22) is the first term containing a zero; this is due to the fact that a(21) is the first term having exactly 10 occurrences of a two-digit number, namely 10 x 32.

			a(0) = 11: 1x99 --> a(1)=199;
a(1) = 199: 1x19 and 1x99 --> a(2)=119199;
a(2) = 119199: 1x11, 2x19, 1x91 and 1x99 --> a(3)=111219191199;
a(3) = 111219191199: 3x11, 1x12, 3x19, 1x21, 2x91 and 1x99 --> a(4)=311112319121291199.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Look and Say Sequence
Wikipedia, Look-and-say sequence
Reinhard Zumkeller, Haskell program for two-digit Look-and-Say sequences

Cf. A005151, A047842.

Cf. A209234 (start=10), A209233 (start=11), A221368 (start=12), A221369 (start=13), A221372 (start=19).

Haskell
```
-- See Link.
```

A112512 Say what you see in previous term, same as A063850, but starting with 2.

Original entry on oeis.org

2, 12, 1112, 3112, 132112, 311322, 232122, 421311, 14123113, 41141223, 24312213, 32142321, 23322114, 32232114, 23322114, 32232114, 23322114, 32232114

Offset: 1

Michele Dondi (blazar(AT)lcm.mi.infn.it), Sep 09 2005

Eventually periodic, eventually identical (to a shift of) A063850.

Cf. A005150, A005151, A063850, A112512-A112516.

#!/usr/bin/perl -l use strict; use warnings; die "Usage: $0  " unless @ARGV==1; $=shift; { print; my (%cnt, %saw); $cnt{$}++ for /./g; s/./ $saw{$&}++ ? '' : $cnt{$&} . $& /ge; <>, redo; } _END_

A010861 Constant sequence: a(n) = 22.

Original entry on oeis.org

22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22

Offset: 0

N. J. A. Sloane

Describe the previous term! (method A - initial term is 22).

Tanya Khovanova, Recursive Sequences
Index to divisibility sequences
Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A005150, A005151.

G.f.: 22/(1-x); e.g.f.: 22*exp(x). - Vincenzo Librandi, Jan 20 2012

A047843 Describe n: give frequency of each digit, by increasing size; mention also missing digits between the smallest and largest one.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1011, 21, 1112, 110213, 11020314, 1102030415, 110203040516, 11020304050617, 1102030405060718, 110203040506070819, 100112, 1112, 22, 1213, 120314, 12030415, 1203040516

Offset: 0

N. J. A. Sloane

Other methods to describe or summarize n are: A047842 (as here, but ignoring "missing" digits), A244112 (count digits in order of decreasing size, ignoring missing digits). - M. F. Hasler, Feb 25 2018

			131 contains two 1's, zero 2's and one 3, so a(131) = 210213.

Vincenzo Librandi, Table of n, a(n) for n = 0..5000

Cf. A005151, A047841, A047842.

a[n_] := Module[{T, f}, T = Tally[IntegerDigits[n]]; f[_] = 0; Do[f[t[[1]]] = t[[2]], {t, T}]; Table[{f[k], k}, {k, Min@T[[All, 1]], Max@T[[All, 1]]} ] // Flatten // FromDigits];
a /@ Range[0, 26] (* Jean-François Alcover, Jan 07 2020 *)

A047843(n,S="")={if(n,for(d=vecmin(n=digits(n)),vecmax(n),S=Str(S,#select(t->t==d,n),d));eval(S),10)} \\ M. F. Hasler, Feb 25 2018

More accurate title from M. F. Hasler, Feb 25 2018

A083671 Array read by rows in which each row describes in words the composition of the previous row.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 1, 2, 2, 1, 3, 2, 1, 2, 2, 2, 3, 1, 1, 4, 2, 1, 3, 3, 1, 1, 2, 1, 3, 1, 4, 4, 1, 1, 2, 2, 3, 1, 4, 3, 1, 2, 2, 1, 3, 2, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4

Offset: 1

N. J. A. Sloane, based on a query from Chasity Engle, Jan 20 2004

Becomes periodic at row 13.

			Array begins:
1
1 1
2 1
1 1 1 2
3 1 1 2
2 1 1 2 1 3
3 1 2 2 1 3
2 1 2 2 2 3
1 1 4 2 1 3
3 1 1 2 1 3 1 4
4 1 1 2 2 3 1 4
3 1 2 2 1 3 2 4
2 1 3 2 2 3 1 4
Explanation: look at 3 1 1 2. What do you see? Two 1's, one 2 and one 3, so the next row is 2 1 1 2 1 3.

Alois P. Heinz, Table of n, a(n) for n = 1..1000
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.

Similar to A005151. Cf. A005150, A034002, A034003.

NestList[Function[test, Flatten[{Count[test, # ], # } & /@ Union[test]]], {1}, 13]
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 ]]; Flatten[ Table[ F[n], {n, 18}]] (* Robert G. Wilson v, Jan 22 2004 *)

G.f.: x*(x^67 -x^65 -x^63 +x^61 -x^59 +x^57 -x^55 +x^53 -x^49 -x^45 -x^44 -x^42 +3*x^41 -x^40 +2*x^38 -x^37 -x^36 +x^35 -x^34 -2*x^33 +2*x^32 -x^30 -x^28 +x^27 +2*x^26 -x^25 -x^24 -x^22 +x^20 -2*x^19 -2*x^18 +2*x^17 -x^13 -x^12 +x^11 -2*x^9 -x^8 -x^7 -x^6 -x^5 -x^4 -2*x^3 -x^2 -x -1) / (x^8-1). - Alois P. Heinz, Jul 25 2013

More terms from Wouter Meeussen and Robert G. Wilson v, Jan 22 2004

A112515 Say what you see in previous term, same as A063850 but starting with 5.

Original entry on oeis.org

5, 15, 1115, 3115, 132115, 31131215, 23411215, 2213143115, 2241231415, 3224311315, 3322143115, 3322311415, 3322311415, 3322311415, 3322311415, 3322311415, 3322311415

Offset: 1

Michele Dondi (blazar(AT)lcm.mi.infn.it), Sep 09 2005

Cf. A005150, A005151, A063850, A112512-A112515.

#!/usr/bin/perl -l use strict; use warnings; die "Usage: $0 " unless @ARGV==1; $=shift; { print; my (%cnt, %saw); $cnt{$}++ for /./g; s/./ $saw{$&}++ ? '' : $cnt{$&} . $& /ge; <>, redo; } _END_

cp's OEIS Frontend

A209233 A two-digit Look-and-Say sequence starting with 11: each term summarizes the increasing two-digit substrings of the previous term.

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A209234 A two-digit Look-and-Say sequence starting with 10: each term summarizes the increasing two-digit substrings of the previous term.

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A221368 A two-digit Look-and-Say sequence starting with 12: each term summarizes the increasing two-digit substrings of the previous term.

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A221372 A two-digit Look-and-Say sequence starting with 19: each term summarizes the increasing two-digit substrings of the previous term.

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A221373 A two-digit Look-and-Say sequence starting with 99: each term summarizes the increasing two-digit substrings of the previous term.

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Haskell

A112512 Say what you see in previous term, same as A063850, but starting with 2.

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Perl

A010861 Constant sequence: a(n) = 22.

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A047843 Describe n: give frequency of each digit, by increasing size; mention also missing digits between the smallest and largest one.

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A083671 Array read by rows in which each row describes in words the composition of the previous row.

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