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.

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A194865 Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {-e}, {-2e}, ..., {-ne}.

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 1, 5, 2, 3, 4, 1, 5, 2, 6, 3, 4, 1, 5, 2, 6, 3, 7, 4, 8, 1, 5, 2, 6, 3, 7, 4, 8, 1, 5, 9, 2, 6, 3, 7, 4, 8, 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 1, 12, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 1, 12, 5, 9, 2, 13, 6, 10, 3, 7, 11, 4, 8
Offset: 1

Views

Author

Clark Kimberling, Sep 04 2011

Keywords

Comments

See A194832 for a general discussion.

Examples

			First nine rows:
1
1 2
1 2 3
4 1 2 3
4 1 5 2 3
4 1 5 2 6 3
4 1 5 2 6 3 7
4 8 1 5 2 6 3 7
4 8 1 5 9 2 6 3 7

Crossrefs

Cf. A194832, A194864, A194866.

Programs

  • Mathematica
    r = -E;
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]  (* A194865 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
{k, 1, n}]]  (* A194866 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194864 *)

A194866 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194865; an interspersion.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 7, 12, 14, 15, 11, 13, 17, 19, 21, 16, 18, 20, 23, 25, 27, 22, 24, 26, 28, 31, 33, 35, 29, 32, 34, 36, 30, 39, 42, 44, 37, 40, 43, 45, 38, 41, 48, 51, 54, 46, 49, 52, 55, 47, 50, 53, 59, 62, 65, 57, 60, 63, 66, 58, 61, 64, 56, 70, 74, 77
Offset: 1

Views

Author

Clark Kimberling, Sep 04 2011

Keywords

Examples

			Northwest corner:
1...2...4...8...12..17..23
3...5...9...14..19..25..33
6...10..15..21..27..35..44
7...11..16..22..29..37..46
13..18..24..32..40..49..60

Crossrefs

Cf. A194832, A194864, A194865.

Programs

  • Mathematica
    r = -E;
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]  (* A194865 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
{k, 1, n}]]  (* A194866 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194864 *)

A194869 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194868; an interspersion.

Original entry on oeis.org

1, 3, 2, 5, 4, 6, 9, 7, 10, 8, 14, 12, 15, 13, 11, 19, 17, 21, 18, 16, 20, 26, 23, 28, 25, 22, 27, 24, 34, 31, 36, 33, 30, 35, 32, 29, 42, 39, 45, 41, 38, 44, 40, 37, 43, 52, 48, 55, 51, 47, 54, 50, 46, 53, 49, 62, 58, 65, 61, 57, 64, 60, 56, 63, 59, 66, 74, 69, 77
Offset: 1

Views

Author

Clark Kimberling, Sep 04 2011

Keywords

Comments

Every pair of rows eventually intersperse.

Examples

			Northwest corner:
1...3...5...9...14..19
2...4...7...12..17..23
6...10..15..21..28..36
8...13..18..25..33..41
11..16..22..30..38..47
20..27..35..44..54..64

Crossrefs

Cf. A194832, A194868, A194870.

Programs

  • Mathematica
    r = -(1 + Sqrt[3])/2;
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]  (* A194868 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
{k, 1, n}]] (* A194869 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]   (* A194870 *)

A194871 Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {r}, {2r}, ..., {nr}, where r=sqrt(6).

Original entry on oeis.org

1, 1, 2, 3, 1, 2, 3, 1, 4, 2, 5, 3, 1, 4, 2, 5, 3, 1, 6, 4, 2, 7, 5, 3, 1, 6, 4, 2, 7, 5, 3, 1, 8, 6, 4, 2, 9, 7, 5, 3, 1, 8, 6, 4, 2, 9, 7, 5, 3, 1, 10, 8, 6, 4, 2, 9, 7, 5, 3, 1, 10, 8, 6, 4, 2, 11, 9, 7, 5, 3, 12, 1, 10, 8, 6, 4, 2, 11, 9, 7, 5, 3, 12, 1, 10, 8, 6, 4, 13, 2, 11, 9, 7, 5
Offset: 1

Views

Author

Clark Kimberling, Sep 04 2011

Keywords

Comments

See A194832 for a general discussion.

Examples

			First nine rows:
1
1 2
3 1 2
3 1 4 2
5 3 1 4 2
5 3 1 6 4 2
7 5 3 1 6 4 2
7 5 3 1 8 6 4 2
9 7 5 3 1 8 6 4 2

Crossrefs

Cf. A194832, A194872, A194873.

Programs

  • Mathematica
    r = Sqrt[6];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]   (* A194871 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
 {k, 1, n}]]   (* A194872 *)
q[n_] := Position[p, n]; Flatten[
Table[q[n], {n, 1, 80}]]   (* A194873 *)

A194872 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194871; an interspersion.

Original entry on oeis.org

1, 2, 3, 5, 6, 4, 8, 10, 7, 9, 13, 15, 12, 14, 11, 18, 21, 17, 20, 16, 19, 25, 28, 24, 27, 23, 26, 22, 32, 36, 31, 35, 30, 34, 29, 33, 41, 45, 40, 44, 39, 43, 38, 42, 37, 50, 55, 49, 54, 48, 53, 47, 52, 46, 51, 60, 65, 59, 64, 58, 63, 57, 62, 56, 61, 66, 72, 77, 70
Offset: 1

Views

Author

Clark Kimberling, Sep 04 2011

Keywords

Comments

See A194832 for a general discussion

Examples

			Northwest corner:
1...2...5...8...13..18
3...6...10..15..21..28
4...7...12..17..24..31
9...14..20..27..35..44
11..16..23..30..39..48

Crossrefs

Cf. A194832, A194872, A194873.

Programs

  • Mathematica
    r = Sqrt[6];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]   (* A194871 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
{k, 1, n}]]   (* A194872 *)
q[n_] := Position[p, n]; Flatten[
Table[q[n], {n, 1, 80}]]   (* A194873 *)

A194874 Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {r}, {2r}, ..., {nr}, where r=-sqrt(6).

Original entry on oeis.org

1, 2, 1, 2, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 5, 2, 4, 6, 1, 3, 5, 2, 4, 6, 1, 3, 5, 7, 2, 4, 6, 8, 1, 3, 5, 7, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 10, 1, 3, 5, 7, 9, 11, 2, 4, 6, 8, 10, 1, 3, 5, 7, 9, 11, 2, 4, 6, 8, 10, 1, 12, 3, 5, 7, 9, 11, 2, 13, 4, 6, 8, 10, 1, 12, 3, 5, 7, 9, 11, 2, 13
Offset: 1

Views

Author

Clark Kimberling, Sep 04 2011

Keywords

Comments

See A194832 for a general discussion.

Examples

			First nine rows:
1
2 1
2 1 3
2 4 1 3
2 4 1 3 5
2 4 6 1 3 5
2 4 6 1 3 5 7
2 4 6 8 1 3 5 7
2 4 6 8 1 3 5 7 9

Crossrefs

Cf. A194832, A194875, A194876.

Programs

  • Mathematica
    r = -Sqrt[6];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]   (* A194874 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
{k, 1, n}]]   (* A194875 *)
q[n_] := Position[p, n]; Flatten[
Table[q[n], {n, 1, 80}]]   (* A194876 *)

A194875 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194874; an interspersion.

Original entry on oeis.org

1, 3, 2, 5, 4, 6, 9, 7, 10, 8, 13, 11, 14, 12, 15, 19, 16, 20, 17, 21, 18, 25, 22, 26, 23, 27, 24, 28, 33, 29, 34, 30, 35, 31, 36, 32, 41, 37, 42, 38, 43, 39, 44, 40, 45, 51, 46, 52, 47, 53, 48, 54, 49, 55, 50, 62, 57, 63, 58, 64, 59, 65, 60, 66, 61, 56, 73, 68, 75
Offset: 1

Views

Author

Clark Kimberling, Sep 04 2011

Keywords

Comments

See A194832 for a general discussion.

Examples

			Northwest corner:
1...3...5...9...13..19
2...4...7...11..16..22
6...10..14..20..26..34
8...12..17..23..30..38
15..21..27..35..43..53

Crossrefs

Cf. A194832, A194874, A194876.

Programs

  • Mathematica
    r = -Sqrt[6];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]   (* A194874 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
{k, 1, n}]]   (* A194875 *)
q[n_] := Position[p, n]; Flatten[
Table[q[n], {n, 1, 80}]]   (* A194876 *)

A194877 Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {r}, {2r}, ..., {nr}, where r=sqrt(8).

Original entry on oeis.org

1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 7, 1, 6, 5, 4, 3, 8, 2, 7, 1, 6, 5, 4, 9, 3, 8, 2, 7, 1, 6, 5, 10, 4, 9, 3, 8, 2, 7, 1, 6, 11, 5, 10, 4, 9, 3, 8, 2, 7, 1, 6, 11, 5, 10, 4, 9, 3, 8, 2, 7, 1, 12, 6, 11, 5, 10, 4, 9, 3, 8, 2, 13, 7, 1, 12, 6, 11, 5, 10
Offset: 1

Views

Author

Clark Kimberling, Sep 04 2011

Keywords

Comments

See A194832 for a general discussion.

Examples

			First nine rows:
1
2 1
3 2 1
4 3 2 1
5 4 3 2 1
5 4 3 2 1 6
5 4 3 2 7 1 6
5 4 3 8 2 7 1 6
5 4 9 3 8 2 7 1 6

Crossrefs

Cf. A194832, A194878, A194879.

Programs

  • Mathematica
    r = Sqrt[8];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]   (* A194877 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
{k, 1, n}]]   (* A194878 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]   (* A194879 *)

A194878 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194877; an interspersion.

Original entry on oeis.org

1, 3, 2, 6, 5, 4, 10, 9, 8, 7, 15, 14, 13, 12, 11, 20, 19, 18, 17, 16, 21, 27, 25, 24, 23, 22, 28, 26, 35, 33, 31, 30, 29, 36, 34, 32, 44, 42, 40, 38, 37, 45, 43, 41, 39, 54, 52, 50, 48, 46, 55, 53, 51, 49, 47, 65, 63, 61, 59, 57, 66, 64, 62, 60, 58, 56, 76, 74, 72
Offset: 1

Views

Author

Clark Kimberling, Sep 04 2011

Keywords

Comments

See A194832 for a general discussion.

Examples

			Northwest corner:
1...3...6...10..15..20..27
2...5...9...14..19..25..33
4...8...13..18..24..31..40
7...12..17..23..30..38..48
11..16..22..29..37..46..57

Crossrefs

Cf. A194832, A194877, A194879.

Programs

  • Mathematica
    r = Sqrt[8];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]   (* A194877 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
{k, 1, n}]]   (* A194878 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]   (* A194879 *)

A194896 Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {r}, {2r}, ..., {nr}, where r=-sqrt(8).

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 7, 2, 3, 4, 5, 6, 1, 7, 2, 8, 3, 4, 5, 6, 1, 7, 2, 8, 3, 9, 4, 5, 6, 1, 7, 2, 8, 3, 9, 4, 10, 5, 6, 1, 7, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 1, 7, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 1, 7, 13, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 1, 7
Offset: 1

Views

Author

Clark Kimberling, Sep 04 2011

Keywords

Comments

See A194832 for a general discussion.

Examples

			First nine rows:
1
1 2
1 2 3
1 2 3 4
1 2 3 4 5
6 1 2 3 4 5
6 1 7 2 3 4 5
6 1 7 2 8 3 4 5
6 1 7 2 8 3 9 4 5

Crossrefs

Cf. A194832, A194897, A194898.

Programs

  • Mathematica
    r = -Sqrt[8];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]] (* A194896 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
{k, 1, n}]] (* A194897 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A194898 *)
Previous Showing 21-30 of 49 results. Next

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