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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A194294 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=2n, r=(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, 1, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 3, 1, 3, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 1, 2, 3, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194285, A194293.

Programs

  • Mathematica
    r = 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[%]    (* A194294 *)

A194295 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^2, r=(1+sqrt(5))/2, the golden ratio.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194295.

Programs

  • Mathematica
    r = 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[%]    (* A194295 *)

A194296 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=2^n, r=(1+sqrt(5))/2, the golden ratio.

Original entry on oeis.org

2, 2, 2, 3, 2, 3, 4, 4, 4, 4, 6, 6, 7, 7, 6, 10, 11, 10, 12, 10, 11, 19, 19, 17, 19, 19, 17, 18, 32, 33, 32, 31, 33, 32, 31, 32, 57, 57, 57, 56, 57, 58, 56, 58, 56, 102, 102, 103, 102, 102, 103, 102, 103, 103, 102, 187, 186, 187, 185, 185, 186, 187, 187, 186, 187
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

			First seven rows:
2
2...2
3...2...3
4...4...4...4
6...6...7...7...6
10..11..10..12..10..11
19..19..17..19..19..17..18

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 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, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194296 *)

A194297 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=(1+sqrt(3))/2.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

			First ten rows:
1
1..1
1..1..1
1..2..1..0
1..1..1..1..1
1..1..2..0..2..0
1..1..1..2..0..2..0
1..1..1..1..1..1..1..1
1..1..1..1..1..1..1..1..1
1..1..1..1..1..1..1..1..1..1

Crossrefs

Cf. A194297.

Programs

  • Mathematica
    r = (1+Sqrt[3])/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}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194297 *)

A194298 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=(1+sqrt(3))/2.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

			First eight rows:
2
3..1
2..2..2
2..2..2..2
2..2..2..2..2
2..2..3..2..2..1
3..1..3..2..1..3..1
3..1..2..3..1..2..3..1

Crossrefs

Cf. A194298.

Programs

  • Mathematica
    r = (1+Sqrt[3])/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[%]    (* A194298 *)

A194299 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=(1+sqrt(3))/2.

Original entry on oeis.org

1, 3, 1, 3, 3, 3, 4, 5, 3, 4, 6, 5, 5, 5, 4, 6, 6, 7, 5, 7, 5, 7, 7, 7, 8, 6, 8, 6, 9, 8, 8, 9, 7, 8, 8, 7, 9, 8, 10, 8, 10, 9, 9, 9, 9, 10, 10, 10, 11, 10, 10, 10, 10, 10, 9, 10, 11, 11, 12, 11, 11, 11, 11, 11, 11, 11, 11, 13, 12, 11, 13, 12, 12, 11, 13, 12, 12, 12, 13, 14, 13
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = (1+Sqrt[3])/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[%]    (* A194299 *)

A194300 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=(1+sqrt(3))/2.

Original entry on oeis.org

2, 3, 1, 2, 3, 3, 4, 5, 3, 4, 6, 7, 6, 7, 6, 11, 11, 12, 9, 11, 10, 19, 17, 19, 19, 17, 20, 17, 32, 32, 33, 32, 32, 32, 32, 31, 58, 56, 57, 57, 57, 57, 57, 57, 56, 103, 102, 102, 103, 103, 102, 101, 103, 103, 102, 186, 187, 185, 186, 187, 187, 185, 186, 187, 187
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

			First six rows:
2
3..1
2..3..3
4..5..3..4
6..7..6..7..6
11..11..12..9...11..10

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = (1+Sqrt[3])/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[%]    (* A194300 *)

A194301 Triangular array: g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

			First nine rows:
1
2..0
1..1..1
1..1..1..1
1..1..1..1..1
0..2..2..0..1..1
0..2..1..1..2..0..1
0..2..0..2..0..2..0..2
0..2..1..1..1..1..1..1..1

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = Sqrt[5];
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[%]    (* A194301 *)

A194302 Triangular array: g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n.

Original entry on oeis.org

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 3, 1, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 3, 2, 1, 3, 2, 1, 2, 2, 3, 2, 1, 3, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 3, 1, 3, 2, 2, 1, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 3, 1
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

			First eight rows:
2
2..2
2..2..2
2..2..2..2
2..2..2..2..2
1..2..3..2..2..2
2..2..3..1..3..1..2
2..2..2..2..2..2..2..2

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = Sqrt[5];
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[%]    (* A194302 *)

A194303 Triangular array: g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 4, 6, 5, 5, 6, 7, 7, 6, 5, 5, 7, 7, 7, 8, 7, 6, 7, 8, 9, 7, 9, 7, 9, 7, 8, 8, 10, 9, 9, 9, 9, 9, 9, 9, 9, 11, 9, 10, 12, 9, 10, 10, 10, 10, 10, 12, 11, 11, 11, 11, 12, 11, 10, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = Sqrt[5];
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[%]    (* A194303 *)
Previous Showing 11-20 of 60 results. Next

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