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 51-60 of 60 results.

A194336 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-tau, where tau=(1+sqrt(5))/2, the golden ratio.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

			First eight rows:
2
2...2
3...2...3
4...4...4...4
6...7...7...6...6
11..10..12..10..11..10
18..17..19..19..17..19..19
32..31..32..33..31..32..33..32

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, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194336 *)

A194337 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=3-sqrt(5).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 3-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[%]    (* A194337 *)

A194338 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=3-sqrt(5).

Original entry on oeis.org

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 1, 3, 1, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 3, 1, 2, 3, 2, 2, 2, 2, 2, 2, 1, 3, 1, 3, 1, 2, 3, 2, 2, 2, 1, 2, 2, 3, 1, 3, 2, 1, 4, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 1, 2, 3, 2, 1, 3
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..3..2..1
2..1..3..1..3..2..2
2..2..2..2..2..2..2..2
1..2..2..2..2..2..3..2..2

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 3-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[%]    (* A194338 *)

A194339 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=3-sqrt(5).

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 4, 5, 5, 5, 6, 7, 7, 6, 7, 6, 7, 8, 7, 7, 7, 8, 7, 9, 7, 9, 7, 9, 8, 9, 9, 9, 9, 9, 9, 9, 10, 8, 10, 10, 10, 10, 9, 12, 10, 9, 11, 9, 11, 11, 10, 11, 12, 11, 11, 11, 11, 12, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14, 12, 14, 12
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..7..7..6
7..6..7..8..7..7..7
8..7..9..7..9..7..9..8

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 3-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[%]    (* A194339 *)

A194340 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=3-sqrt(5).

Original entry on oeis.org

2, 2, 2, 3, 3, 2, 4, 4, 4, 4, 6, 6, 7, 6, 7, 11, 10, 10, 11, 11, 11, 18, 19, 17, 19, 18, 19, 18, 32, 31, 32, 31, 33, 32, 33, 32, 57, 57, 56, 57, 57, 57, 57, 58, 56, 102, 102, 103, 102, 101, 105, 102, 102, 102, 103, 187, 184, 188, 185, 186, 187, 186, 187, 185, 188
Offset: 1

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

			First six rows:
2
2...2
3...3...2
4...4...4...4
6...6...7...6...7
11..10..10..11..11..11

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 3-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, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194340 *)

A194341 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=3-e.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A193285.

Programs

  • Mathematica
    r = 3-E;
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[%]    (* A194341 *)

A194342 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=3-e.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 3-E;
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[%]    (* A194342 *)

A194343 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=3-e.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194343.

Programs

  • Mathematica
    r = 3-E;
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[%]    (* A194343 *)

A194344 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=3-e.

Original entry on oeis.org

2, 2, 2, 3, 2, 3, 3, 4, 5, 4, 7, 6, 6, 7, 6, 10, 11, 11, 11, 11, 10, 19, 19, 18, 18, 18, 18, 18, 32, 32, 33, 32, 32, 31, 32, 32, 56, 56, 59, 56, 57, 57, 56, 58, 57, 102, 102, 103, 102, 102, 103, 103, 101, 102, 104, 185, 187, 186, 186, 187, 185, 187, 186, 186, 186
Offset: 1

Views

Author

Clark Kimberling, Aug 22 2011

Keywords

Comments

See A194285.

Examples

			First eight rows:
2
2...2
3...2...3
3...4...5...4
7...6...6...7...6
10..11..11..11..11..10
19..19..18..18..18..18..18
32..32..33..32..32..31..32..32

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 3-E;
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[%]    (* A194344 *)

A194306 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= 2n, 1 <= k <= n.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

			First nine rows:
  3;
  3, 1;
  2, 2, 2;
  2, 2, 2, 2;
  2, 2, 3, 1, 2;
  2, 2, 2, 2, 2, 2;
  2, 2, 2, 2, 2, 2, 2;
  1, 2, 3, 2, 2, 2, 2, 2;
  0, 3, 3, 3, 1, 2, 2, 2, 2;

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = Pi;
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[%]    (* A194305 *)
Previous Showing 51-60 of 60 results.

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