A047842 -id:A047842 - cp's OEIS frontend

A221369 A two-digit Look-and-Say sequence starting with 13: each term summarizes the increasing two-digit substrings of the previous term.

13, 113, 111113, 411113, 311113141, 311113114231141, 511113214123331141142, 511112113314121123131132233241142151, 711312313214115321122223124331232233241142251, 411412213214115221522423224125431432233241142143151153171

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 42.

			a(0) = 11: 1 x 13 --> a(1) = 113;
a(1) = 113: 1 x 11 and 1 x 13 --> a(2) = 111113;
a(2) = 111113: 4 x 11 and 1 x 13 --> a(3) = 411113;
a(3) = 411113: 3 x 11, 1 x 13 and 1 x 41 --> a(4) = 311113141.

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), A221372 (start=19), A221373 (start=99).

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

A036058 Summarize digits of preceding number, by decreasing digit value. Start with a(0) = 0.

Original entry on oeis.org

0, 10, 1110, 3110, 132110, 13123110, 23124110, 1413223110, 1423224110, 2413323110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110

Offset: 0

Floor van Lamoen

This kind of counting sequence is always eventually periodic with period 1, 2 or 3. - Herve Lehning (lehning(AT)noos.fr), Oct 01 2003

			The third term is 1110 because the second term contains one 1 and one 0.

Herve Lehning, Computer-aided or analytic proof?, College Mathematics Journal, Vol. 21, No. 3, 1990, pp. 228-239.
Index of eventually constant sequences.

Cf. A007890 (same as this, starting at 1), A001155 (same as this, but using method A047842: by increasing digit value), A005150 (as before, starting at 1), A036059 ("fibonacci" based on this), A036066.

a(n)=if(n>9,1433223110,[0,10,1110,3110,132110,13123110,23124110,1413223110, 1423224110,2413323110][n+1]) \\ Charles R Greathouse IV, Jul 24 2012

a(n,a=0)={for(k=1,n,a==(a=A244112(a))&&break);a} \\ M. F. Hasler, Feb 25 2018

a(n+1) = A244112(a(n)), a(0) = 0. - M. F. Hasler, Feb 25 2018

A023989 Look and Say sequence: describe the previous term! (method C - initial term is 2).

Original entry on oeis.org

2, 12, 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, 21322314

Offset: 0

Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), Mar 19 2002

Method C = 'frequency' followed by 'digit'-indication with digits in increasing order.
Converges to 21322314 at the eleventh term.
Depending on the initial value, the sequence may converge to a cycle of 2 or more values, for example: 123456, 111213141516, 711213141516, 61121314151617, 71121314152617, 61221314151627, 51321314152617, 51222314251617, 41421314251617, 51221334151617, 51222314251617, 41421314251617, 51221334151617. [Corrected by Pontus von Brömssen, Jun 04 2023]
a(n) = A005151(n) for n > 6. - Reinhard Zumkeller, Jan 26 2014

			a(1) = 12, so a(2) = 1112 because 12 contains a digit 1 and a digit 2; a(3) = 3112 because 1112 contains three digits 1 and a digit 2

Cf. A005150, A005151, A022481.

Cf. A047842, A118628.

import Data.List (group, sort, transpose)
a023989 n = a023989_list !! (n-1)
a023989_list = 2 : f [2] :: [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) = A047842(a(n-1)). - Pontus von Brömssen, Jun 04 2023

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

Original entry on oeis.org

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.
```

A036066 The summarize Lucas sequence: summarize the previous two terms, start with 1, 3.

Original entry on oeis.org

1, 3, 1311, 2331, 331241, 14432231, 34433241, 54533231, 2544632221, 163534435221, 263544436231, 363554634231, 463554733221, 17364544733221, 37263554634231, 37363554734231, 37364544933221, 1937263554933221, 3927263544835231, 391827264534836231, 293827363544836231

Offset: 0

Floor van Lamoen

After the 26th term the sequence goes into a cycle of 46 terms.

"Summarize" uses here method C = A244112: in order of decreasing digit value.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index to sequences related to say what you see

Cf. A036059.

Cf. A244112 (summarizing as used here: by decreasing digit value), A047842 (alternative summarizing method: by increasing digit value), A047843 (another method: don't omit missing digits between smallest and largest one).

a:= proc(n) option remember; `if`(n<2, 2*n+1, (p-> parse(cat(seq((c->
     `if`(c=0, [][], [c, 9-i][]))(coeff(p, x, 9-i)), i=0..9))))(
      add(x^i, i=map(x-> convert(x, base, 10)[], [a(n-1),a(n-2)]))))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Jun 18 2022

a[0] = 1; a[1] = 3; a[n_] := a[n] = FromDigits @ Flatten @ Reverse @ Select[ Transpose @ { DigitCount[a[n-1]] + DigitCount[a[n-2]], Append[ Range[9], 0]}, #[[1]] > 0 &];
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Dec 30 2017 *)

{a=[1,3]; for(n=1,50,a=concat(a,A244112(eval(Str(a[n],a[n+1]))))); a} \\ M. F. Hasler, Feb 25 2018

a(n+1) = A244112(concat(a(n),a(n-1))). - M. F. Hasler, Feb 25 2018

A127355 Primes with prime digit counts. The digit count numerically summarizes the frequency of digits 0 through 9 in that order when they occur in a number.

Original entry on oeis.org

3, 7, 17, 23, 71, 101, 103, 107, 109, 113, 127, 131, 137, 173, 199, 223, 233, 271, 311, 313, 317, 331, 359, 367, 409, 479, 499, 593, 673, 677, 701, 709, 773, 797, 907, 919, 929, 947, 953, 977, 991, 1009, 1123, 1129, 1193, 1213, 1217, 1223, 1231, 1277, 1291

Offset: 1

Lekraj Beedassy, Jan 11 2007

Compare with "Look And Say" version A056815.

			The primes 479,991,1747 respectively have digit counts 141719 (one 4,one 7,one 9), 1129 (one 1, two 9's), 111427 (one 1, one 4, two 7's) which are also prime; So they belong to the sequence.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A047842, A127354.

a127355 n = a127355_list !! (n-1)
a127355_list = filter ((== 1) . a010051' . a047842) a000040_list
-- Reinhard Zumkeller, Apr 14 2014

dc[n_] :=FromDigits@Flatten@Select[Table[{DigitCount[n, 10, k], k}, {k, 0, 9}], #[[1]] > 0 &];Select[Prime@Range[210], PrimeQ[dc[ # ]] &] (* Ray Chandler, Jan 16 2007 *)

A010051(a(n)) * A010051(A047842(a(n))) = 1. - Reinhard Zumkeller, Apr 14 2014

Corrected by Ray Chandler, Jan 16 2007

cp's OEIS Frontend

A221369 A two-digit Look-and-Say sequence starting with 13: each term summarizes the increasing two-digit substrings of the previous term.

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A036058 Summarize digits of preceding number, by decreasing digit value. Start with a(0) = 0.

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A023989 Look and Say sequence: describe the previous term! (method C - initial term is 2).

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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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