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 41-50 of 60 results. Next

A194326 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n, r=2-sqrt(2).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

			First ten rows:
2
2..2
1..3..2
2..1..3..2
2..2..2..2..2
2..2..2..2..2..2
2..3..1..2..3..1..2
2..2..3..1..3..1..3..1
2..2..1..3..2..2..2..2..2
1..3..2..2..1..3..2..3..1..2

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 2-Sqrt[2];
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, 2n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194326 *)

A194327 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=2-sqrt(2).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 2-Sqrt[2];
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194327 *)

A194328 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n, r=2-sqrt(2).

Original entry on oeis.org

2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 6, 6, 7, 7, 6, 10, 11, 10, 11, 11, 11, 18, 18, 18, 18, 19, 18, 19, 32, 32, 32, 31, 33, 31, 33, 32, 57, 57, 56, 57, 57, 57, 58, 56, 57, 101, 103, 102, 103, 101, 104, 102, 103, 102, 103, 185, 188, 186, 186, 185, 187, 187, 186, 187, 184
Offset: 1

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

			First eight rows:
2
2...2
2...3...3
4...4...4...4
6...6...7...7...6
10..11..10..11..11..11
18..18..18..18..19..18..19
32..32..32..31..33..31..33..32

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 2-Sqrt[2];
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194328 *)

A194329 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n, r=2-sqrt(3).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

			First eleven rows:
1
1..1
1..1..1
1..1..1..1
1..2..1..0..1
1..1..1..2..1..0
1..1..1..1..1..1..1
1..1..2..0..2..0..1..1
1..1..1..2..1..1..0..2..0
1..1..1..1..1..1..2..0..2..0
1..1..1..1..1..1..1..1..1..1..1

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 2-Sqrt[3];
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194329 *)

A194330 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n, r=2-sqrt(3).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

			First nine rows:
2
2..2
2..3..1
2..2..2..2
2..2..2..2..2
2..2..2..2..2..2
1..3..2..2..2..2..2
2..2..3..2..2..1..2..2
2..2..2..2..3..1..2..3..1

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 2-Sqrt[3];
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, 2n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194330 *)

A194331 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=2-sqrt(3).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 2-Sqrt[3];
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194331 *)

A194332 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n, r=2-sqrt(3).

Original entry on oeis.org

2, 2, 2, 3, 3, 2, 4, 5, 3, 4, 6, 7, 7, 6, 6, 12, 10, 10, 12, 10, 10, 18, 19, 19, 18, 18, 18, 18, 32, 31, 34, 31, 33, 31, 32, 32, 57, 58, 57, 57, 56, 57, 57, 57, 56, 103, 102, 103, 103, 102, 103, 102, 101, 104, 101, 186, 186, 187, 187, 186, 186, 186, 186, 186, 186
Offset: 1

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

			First eight rows:
2
2...2
3...3...2
4...5...3...4
6...7...7...6...6
12..10..10..12..10..10
18..19..19..18..18..18..18
32..31..34..31..33..31..32..32

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 2-Sqrt[3];
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194332 *)

A194333 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

			First eleven rows:
1
1..1
1..1..1
1..1..1..1
1..1..1..1..1
1..1..1..1..1..1
0..1..2..1..1..1..1
1..1..1..1..1..1..1..1
1..1..1..2..1..0..2..0..1
1..1..1..1..1..1..1..1..1..1
1..1..1..1..2..1..0..1..1..1..1

Crossrefs

Cf. A194333.

Programs

  • Mathematica
    r = 2-GolenRatio;
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194333 *)

A194334 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

			First nine rows:
2
2..2
2..2..2
2..2..2..2
2..2..2..2..2
2..2..2..2..3..1
1..2..3..2..2..2..2
2..2..2..2..2..2..2..2
1..3..1..3..2..1..3..2..2

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 2-GoldenRatio;
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, 2n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194334 *)

A194335 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 2-GoldenRatio;
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194335 *)
Previous Showing 41-50 of 60 results. Next

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

Content is available under The OEIS End-User License Agreement.