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.

Previous Showing 21-25 of 25 results.

A105062 Triangle read by rows, based on the morphism f: 1->2, 2->3, 3->4, 4->5, 5->6, 6->{6,6,10,7}, 7->8, 8->9, 9->10, 10->11, 11->12, 12->{12,12,5,1}. First row is 1. If current row is a,b,c,..., then the next row is a,b,c,...,f(a),f(b),f(c),...

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4
Offset: 0

Views

Author

Roger L. Bagula, Apr 05 2005

Keywords

Comments

11's and 12's do not show up until the 8th iteration, below that it resembles the lower bi-Kenyons
Level 6 bi-Kenyon substitution sequence.

Links

Crossrefs

Cf. A000120, A073058.

Programs

  • Mathematica
    s[n_] := n /. {1 -> 2, 2 -> 3, 3 -> 4, 4 -> 5, 5 -> 6, 6 -> {6, 6, 10, 7}, 7 -> 8, 8 -> 9, 9 -> 10, 10 -> 11, 11 -> 12, 12 -> {12, 12, 5, 1}}; t[a_] := Join[a, Flatten[s /@ a]]; Flatten[ NestList[t, {1}, 6]]

A105102 A bi-Minimal Pisot substitution.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 5, 4, 1, 2, 2, 3, 2, 3, 3, 5, 4, 2, 3, 3, 5, 4, 3, 5, 4, 5, 4, 6, 5, 1, 2, 2, 3, 2, 3, 3, 5, 4, 2, 3, 3, 5, 4, 3, 5, 4, 5, 4, 6, 5, 2, 3, 3, 5, 4, 3, 5, 4, 5, 4, 6, 5, 3, 5, 4, 5, 4, 6, 5, 5, 4, 6, 5, 6, 5, 2, 1, 6, 1, 2, 2, 3, 2, 3, 3, 5, 4, 2, 3, 3, 5, 4, 3, 5, 4, 5, 4
Offset: 0

Views

Author

Roger L. Bagula, Apr 07 2005

Keywords

Crossrefs

Cf. A073058.

Programs

  • Mathematica
    s[1] = {2}; s[2] = {3}; s[3] = {5, 4}; s[4] = {5}; s[5] = {6}; s[6] = {2, 1}; t[a_] := Join[a, Flatten[s /@ a]]; p[0] = {1}; p[1] = t[{1}]; p[n_] := t[p[n - 1]] aa = Flatten[Table[p[n], {n, 0, 6}]]

Formula

1-> 2 2->3 3->{5, 4} 4->5 5->6 6->{2, 1}

A105103 A bi-Rauzy Pisot substitution.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 6, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 6, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 6, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 6, 1, 2, 1, 3, 1, 2, 6, 1, 2, 1, 3, 1
Offset: 0

Views

Author

Roger L. Bagula, Apr 07 2005

Keywords

Crossrefs

Cf. A073058, A103684.

Programs

  • Mathematica
    s[1] = {1, 2}; s[2] = {1, 3}; s[3] = {6}; s[4] = {4, 5}; s[5] = {4, 6}; s[6] = {1}; t[a_] := Join[a, Flatten[s /@ a]]; p[0] = {1}; p[1] = t[{1}]; p[n_] := t[p[n - 1]] aa = Flatten[Table[p[n], {n, 0, 6}]]

Formula

1->{1, 2} 2->{1, 3} 3->6 4->{4, 5} 5->{4, 6) 6->1

A105164 Triangle read by rows, based on the morphism f: 1->2, 2->3, 3->4, 4->5, 5->{5,9,7,6}, 6->7, 7->8, 8->9, 9->10, 10->{10,4,2,1}. First row is 1. If current row is a,b,c,..., then the next row is a,b,c,...,f(a),f(b),f(c),...

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 5, 9, 7, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 5, 9, 7, 6, 2, 3, 3, 4
Offset: 0

Views

Author

Roger L. Bagula, Apr 09 2005

Keywords

Comments

A ten-symbol substitution based on a bi-Kenyon-like sign symmetry substitution for the Pisot-Vijayaraghavan constant: x^5-x^3-x-1=0.

Crossrefs

Cf. A105061, A000120, A073058.

Programs

  • Mathematica
    s[n_] := n /. {1 -> 2, 2 -> 3, 3 -> 4, 4 -> 5, 5 -> {5, 9, 7, 6}, 6 -> 7, 7 -> 8, 8 -> 9, 9 -> 10, 10 -> {10, 4, 2, 1}}; t[a_] := Join[a, Flatten[s /@ a]]; Flatten[ NestList[t, {1}, 6]]

Extensions

Edited by N. J. A. Sloane, Jun 16 2007

A105258 Triangle of trajectory of 1 under the morphism 1->2, 2->13, 3->1.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1, 1, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1, 2, 1, 3, 1, 3, 2, 1, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1, 2, 1, 3, 1, 3, 2, 1, 1, 3, 2, 1, 2, 1, 1, 3, 2, 2, 1, 3, 1, 3, 2, 1, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 3, 2, 1, 2, 1, 1, 3, 2, 2, 1, 1, 3
Offset: 0

Views

Author

Roger L. Bagula, Apr 14 2005

Keywords

Examples

			The first steps are:
{1}
{1, 2}
{1, 2, 2, 1, 3}
{1, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1}

Links

Crossrefs

Cf. A073058, A105111.

Programs

  • Mathematica
    s[1] = {2}; s[2] = {1, 3}; s[3] = {1}; t[a_] := Join[a, Flatten[s /@ a]]; p[0] = {1}; p[1] = t[{1}]; p[n_] := t[p[n - 1]] aa = Flatten[Table[p[n], {n, 0, 6}]]
  • PARI
    {a(n)=local(m, v, w); v=w=[1]; while(length(w)

Extensions

Edited by the Associate Editors of the OEIS, Apr 07 2009
Previous Showing 21-25 of 25 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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