cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

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

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Author

Keywords

Comments

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

Examples

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

References

  • 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).

Crossrefs

Programs

Formula

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

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Author

Keywords

Comments

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

Examples

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

Crossrefs

Programs

Formula

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

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Author

Keywords

Comments

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

Examples

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

Crossrefs

Programs

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

Formula

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

Extensions

More terms from Erich Friedman

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

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Author

Keywords

Comments

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

Examples

			E.g., the term after 1911 is obtained by saying "two 1's, one 9, one 1", which gives 211911.
		

Crossrefs

Extensions

More terms from Erich Friedman

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

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Author

Keywords

Comments

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

Examples

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

Crossrefs

Programs

Extensions

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

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Author

Keywords

Comments

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

Examples

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

Crossrefs

Programs

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

Extensions

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

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Author

Keywords

Comments

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

Examples

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

Crossrefs

Programs

  • Mathematica
    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 *)

Extensions

More terms from Erich Friedman

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

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Author

Keywords

Comments

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

Examples

			The term after 1511 is obtained by saying "two 1's, one 5, one 1", which gives 211511.
		

Crossrefs

Extensions

More terms from Erich Friedman

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

Views

Author

Keywords

Comments

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

Examples

			E.g., the term after 1611 is obtained by saying "two 1's, one 6, one 1", which gives 211611.
		

Crossrefs

Programs

  • Mathematica
    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 *)
  • Python
    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

Extensions

More terms from Erich Friedman
Showing 1-9 of 9 results.