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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A194304 Triangular array: g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

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

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, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194304 *)

A194307 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= n^2, 1 <= k <= n.

Original entry on oeis.org

1, 3, 1, 4, 2, 3, 3, 5, 4, 4, 4, 5, 7, 3, 6, 6, 5, 5, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 8, 9, 9, 9, 8, 9, 8, 11, 10, 8, 7, 9, 11, 10, 10, 10, 11, 9, 9, 12, 9, 9, 11, 10, 12, 10, 12, 11, 10, 11, 12, 10, 11, 12, 9, 14, 11, 13, 14, 10, 13, 10, 13, 12, 11, 14, 8, 17, 11, 14
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

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

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^2}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194307 *)

A194308 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= 2^n, 1 <= k <= n.

Original entry on oeis.org

2, 3, 1, 3, 2, 3, 3, 5, 4, 4, 5, 7, 8, 4, 8, 10, 9, 10, 12, 12, 11, 19, 18, 18, 18, 18, 18, 19, 31, 31, 32, 32, 32, 32, 32, 34, 53, 58, 55, 61, 55, 57, 53, 60, 60, 99, 100, 100, 108, 100, 100, 108, 100, 100, 109, 180, 182, 180, 200, 182, 180, 182, 200, 180, 182
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

			First six rows:
   2;
   3,  1;
   3,  2,  3;
   3,  5,  4,  4;
   5,  7,  8,  4,  8;
  10,  9, 10, 12, 12, 11;

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, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194308 *)

A194309 Triangular array: g(n,k)=number of fractional parts (i*e) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

			1
1..1
1..1..1
1..1..1..1
1..0..2..1..1
1..1..1..1..1..1
1..1..1..1..1..1..1
1..1..1..1..1..2..1..0

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 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[%]    (* A194309 *)

A194310 Triangular array: g(n,k)=number of fractional parts (i*e) 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, 3, 1, 3, 1, 3, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 1, 2, 3, 1, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 3, 1, 2, 3, 1, 2, 3, 1, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 3, 1, 2, 3, 1, 3, 2, 2, 2, 1, 2, 1, 3, 1, 3, 1, 3, 1, 3, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1
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..3..1
3..1..3..2..1
2..2..2..2..2..2
2..2..2..2..2..2..2
2..2..2..3..2..2..2..1
2..3..1..2..2..2..3..1..2

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 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[%]    (* A194310 *)

A194311 Triangular array: g(n,k)=number of fractional parts (i*e) 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, 5, 4, 3, 5, 5, 5, 5, 5, 6, 5, 7, 5, 7, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 10, 9, 9, 9, 9, 10, 9, 8, 10, 10, 9, 11, 10, 9, 10, 10, 11, 10, 11, 11, 11, 10, 12, 10, 12, 10, 12, 11, 11, 11, 12, 12, 11, 12, 13, 12, 12, 13, 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..5..4..3
5..5..5..5..5
6..5..7..5..7..6
7..7..7..7..7..7..7
8..8..8..8..8..8..8..8

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 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[%]    (* A194311 *)

A194312 Triangular array: g(n,k)=number of fractional parts (i*e) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = 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[%]    (* A194312 *)

A194313 Triangular array: g(n,k)=number of fractional parts (i*sqrt(6)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = Sqrt[6];
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[%]    (* A194313 *)

A194314 Triangular array: g(n,k)=number of fractional parts (i*sqrt(6)) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

			First nine rows:
2
2..2
1..2..3
2..2..2..2
2..2..3..2..1
2..1..4..1..2..2
1..2..3..2..2..2..2
1..3..2..3..1..2..2..2
2..2..2..2..2..2..2..2..2

Crossrefs

Cf. A194285.

Programs

  • Mathematica
    r = Sqrt[6];
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[%]    (* A194314 *)

A194315 Triangular array: g(n,k)=number of fractional parts (i*sqrt(6)) 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, 5, 3, 4, 4, 6, 5, 5, 5, 5, 6, 8, 4, 7, 6, 7, 7, 6, 7, 8, 7, 7, 6, 9, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 11, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 14, 10, 12, 13, 12, 12, 12, 13, 13, 12
Offset: 1

Views

Author

Clark Kimberling, Aug 21 2011

Keywords

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194315.

Programs

  • Mathematica
    r = Sqrt[6];
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[%]    (* A194315 *)
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