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.

Showing 1-10 of 10 results.

A376952 a(n) = least k such that (n*Pi/2)^(2k)/(2 k)! < 1.

Original entry on oeis.org

1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 23, 25, 27, 29, 31, 33, 35, 37, 39, 42, 44, 46, 48, 50, 52, 54, 56, 59, 61, 63, 65, 67, 69, 71, 73, 76, 78, 80, 82, 84, 86, 88, 91, 93, 95, 97, 99, 101, 103, 105, 108, 110, 112, 114, 116, 118, 120, 122, 125, 127, 129
Offset: 0

Views

Author

Clark Kimberling, Oct 12 2024

Keywords

Comments

The numbers (n*Pi/2)^(2k)/(2 k)! are the coefficients in the Maclaurin series for cos x when x = n*Pi/2. If m>a(n), then (m*Pi/2)^(2k)/(2 k)! < 1. A375057 is a bisection of this sequence.

Crossrefs

Cf. A370507, A376953, A376954, A376955, A376956, A376957, A376958, A376959, A376960.

Programs

  • Mathematica
    a[n_] := Select[Range[300], (n Pi/2)^(2 #)/(2 #)! < 1 &, 1];
Flatten[Table[a[n], {n, 0, 200}]]

Formula

a(n) ~ Pi*exp(1)*n/4 - log(n)/4. - Vaclav Kotesovec, Oct 13 2024

A376953 a(n) = least k such that (n*Pi/3)^(2k)/(2 k)! < 1.

Original entry on oeis.org

1, 1, 2, 4, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 20, 22, 23, 25, 26, 27, 29, 30, 32, 33, 35, 36, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 52, 53, 54, 56, 57, 59, 60, 61, 63, 64, 66, 67, 69, 70, 71, 73, 74, 76, 77, 78, 80, 81, 83, 84, 86, 87, 88, 90, 91, 93
Offset: 0

Views

Author

Clark Kimberling, Oct 12 2024

Keywords

Comments

The numbers (n*Pi/3)^(2k)/(2 k)! are the coefficients in the Maclaurin series for cos x when x = n*Pi/3. If m>a(n), then (m*Pi/3)^(2k)/(2 k)! < 1. A375057 is a trisection of this sequence.

Crossrefs

Cf. A370507, A376952, A376954, A376955, A376956, A376957, A376958, A376959, A376960.

Programs

  • Mathematica
    a[n_] := Select[Range[300], (n Pi/3)^(2 #)/(2 #)! < 1 &, 1];
Flatten[Table[a[n], {n, 0, 200}]]

Formula

a(n) ~ Pi*exp(1)*n/6 - log(n)/4. - Vaclav Kotesovec, Oct 13 2024

A376954 a(n) = least k such that (2n*Pi/3)^(2k)/(2 k)! < 1.

Original entry on oeis.org

1, 2, 5, 8, 11, 13, 16, 19, 22, 25, 27, 30, 33, 36, 39, 42, 44, 47, 50, 53, 56, 59, 61, 64, 67, 70, 73, 76, 78, 81, 84, 87, 90, 93, 95, 98, 101, 104, 107, 110, 113, 115, 118, 121, 124, 127, 130, 132, 135, 138, 141, 144, 147, 149, 152, 155, 158, 161, 164, 167
Offset: 0

Views

Author

Clark Kimberling, Oct 12 2024

Keywords

Comments

The numbers (2n*Pi/3)^(2k)/(2 k)! are the coefficients in the Maclaurin series for cos x when x = 2n*Pi/3. If m>a(n), then (2m*Pi/3)^(2k)/(2 k)! < 1. A375057 is a trisection of this sequence.

Crossrefs

Cf. A370507, A376952, A376953, A376955, A376956, A376957, A376958, A376959, A376960.

Programs

  • Mathematica
    a[n_] := Select[Range[200], (2n Pi/3)^(2 #)/(2 #)! < 1 &, 1];
Flatten[Table[a[n], {n, 0, 200}]]

Formula

a(n) ~ Pi*exp(1)*n/3 - log(n)/4. - Vaclav Kotesovec, Oct 13 2024

A376955 a(n) = least k such that (3n*Pi/4)^(2k)/(2 k)! < 1.

Original entry on oeis.org

1, 3, 6, 9, 12, 15, 18, 21, 25, 28, 31, 34, 37, 41, 44, 47, 50, 53, 56, 60, 63, 66, 69, 72, 76, 79, 82, 85, 88, 92, 95, 98, 101, 104, 108, 111, 114, 117, 120, 124, 127, 130, 133, 136, 140, 143, 146, 149, 152, 156, 159, 162, 165, 168, 172, 175, 178, 181, 184
Offset: 0

Views

Author

Clark Kimberling, Oct 12 2024

Keywords

Comments

The numbers (3n*Pi/4)^(2k)/(2 k)! are the coefficients in the Maclaurin series for cos x when x = 3n*Pi/4. If m>a(n), then (3m*Pi/4)^(2k)/(2 k)! < 1.

Crossrefs

Cf. A370507, A376952, A376953, A376954, A376956, A376957, A376958, A376959, A376960.

Programs

  • Mathematica
    a[n_] := Select[Range[200], (3n Pi/4)^(2 #)/(2 #)! < 1 &, 1];
Flatten[Table[a[n], {n, 0, 200}]]

Formula

a(n) ~ 3*Pi*exp(1)*n/8 - log(n)/4. - Vaclav Kotesovec, Oct 13 2024

A376957 a(n) = least k such that (n Pi/2)^(2k+1)/(2k+1)! < 1.

Original entry on oeis.org

1, 1, 3, 5, 7, 9, 11, 14, 16, 18, 20, 22, 24, 26, 28, 30, 33, 35, 37, 39, 41, 43, 45, 47, 50, 52, 54, 56, 58, 60, 62, 64, 67, 69, 71, 73, 75, 77, 79, 82, 84, 86, 88, 90, 92, 94, 96, 99, 101, 103, 105, 107, 109, 111, 113, 116, 118, 120, 122, 124, 126, 128
Offset: 0

Views

Author

Clark Kimberling, Oct 17 2024

Keywords

Comments

The numbers (n Pi/2)^(2k+1)/(2k+1)! are the coefficients in the Maclaurin series for sin x when x = Pi/2. If m>a(n), then (n Pi/2)^(2k+1)/(2k+1)! < 1.

Crossrefs

Cf. A370507, A376284, A376952, A376953, A376954, A376955, A376956, A376958, A376959, A376960.

Programs

  • Mathematica
    a[n_] := Select[Range[z], (n Pi/2)^(2 # + 1)/(2 # + 1)! < 1 &, 1]
Flatten[Table[a[n], {n, 0, 100}]]

A376958 a(n) = least k such that (n Pi/3)^(2k+1)/(2k+1)! < 1.

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 16, 17, 19, 20, 21, 23, 24, 26, 27, 28, 30, 31, 33, 34, 35, 37, 38, 40, 41, 43, 44, 45, 47, 48, 50, 51, 52, 54, 55, 57, 58, 60, 61, 62, 64, 65, 67, 68, 69, 71, 72, 74, 75, 77, 78, 79, 81, 82, 84, 85, 86, 88, 89, 91, 92
Offset: 0

Views

Author

Clark Kimberling, Oct 17 2024

Keywords

Comments

The numbers (n Pi/3)^(2k+1)/(2k+1)! are the coefficients in the Maclaurin series for sin x when x = Pi/3. If m>a(n), then (n Pi/3)^(2k+1)/(2k+1)! < 1.

Crossrefs

Cf. A370507, A376284, A376952, A376953, A376954, A376955, A376956, A376957, A376959, A376960.

Programs

  • Mathematica
    a[n_] := Select[Range[z], (n Pi/3)^(2 # + 1)/(2 # + 1)! < 1 &, 1]
Flatten[Table[a[n], {n, 0, 100}]]

A376959 a(n) = least k such that (2n Pi/3)^(2k+1)/(2k+1)! < 1.

Original entry on oeis.org

1, 2, 5, 7, 10, 13, 16, 19, 21, 24, 27, 30, 33, 35, 38, 41, 44, 47, 50, 52, 55, 58, 61, 64, 67, 69, 72, 75, 78, 81, 84, 86, 89, 92, 95, 98, 101, 104, 106, 109, 112, 115, 118, 121, 123, 126, 129, 132, 135, 138, 140, 143, 146, 149, 152, 155, 157, 160, 163, 166
Offset: 0

Views

Author

Clark Kimberling, Oct 17 2024

Keywords

Comments

The numbers (2n Pi/3)^(2k+1)/(2k+1)! are the coefficients in the Maclaurin series for sin x when x = 2Pi/3. If m>a(n), then (n 2Pi/3)^(2k+1)/(2k+1)! < 1.

Crossrefs

Cf. A370507, A376284, A376952, A376953, A376954, A376955, A376956, A376957, A376958, A376960.

Programs

  • Mathematica
    a[n_] := Select[Range[z], (2n Pi/3)^(2 # + 1)/(2 # + 1)! < 1 &, 1]
Flatten[Table[a[n], {n, 0, 100}]]

A376960 a(n) = least k such that (3n Pi/4)^(2k+1)/(2k+1)! < 1.

Original entry on oeis.org

1, 2, 5, 8, 11, 15, 18, 21, 24, 27, 30, 34, 37, 40, 43, 46, 50, 53, 56, 59, 62, 66, 69, 72, 75, 78, 82, 85, 88, 91, 94, 97, 101, 104, 107, 110, 113, 117, 120, 123, 126, 129, 133, 136, 139, 142, 145, 149, 152, 155, 158, 161, 165, 168, 171, 174, 177, 181, 184
Offset: 0

Views

Author

Clark Kimberling, Oct 17 2024

Keywords

Comments

The numbers (3n Pi/4)^(2k+1)/(2k+1)! are the coefficients in the Maclaurin series for sin x when x = 3Pi/4. If m>a(n), then (n 3Pi/4)^(2k+1)/(2k+1)! < 1.

Crossrefs

Cf. A370507, A376284, A376952, A376953, A376954, A376955, A376956, A376957, A376958, A376959.

Programs

  • Mathematica
    a[n_] := Select[Range[z], (3n Pi/4)^(2 # + 1)/(2 # + 1)! < 1 &, 1]
Flatten[Table[a[n], {n, 0, 100}]]

A376284 a(n) = least k such that (2n)^(2k)/(2 k)! < 1.

Original entry on oeis.org

1, 2, 5, 7, 10, 13, 15, 18, 21, 24, 26, 29, 32, 34, 37, 40, 42, 45, 48, 51, 53, 56, 59, 61, 64, 67, 69, 72, 75, 78, 80, 83, 86, 88, 91, 94, 97, 99, 102, 105, 107, 110, 113, 116, 118, 121, 124, 126, 129, 132, 135, 137, 140, 143, 145, 148, 151, 154, 156, 159
Offset: 0

Views

Author

Clark Kimberling, Oct 17 2024

Keywords

Comments

The numbers (2n)^(2k)/(2 k)! are the coefficients in the Maclaurin series for cos x when x = 2. If m>a(n), then (2n)^(2k)/(2 k)! < 1.

Crossrefs

Cf. A370507, A376952, A376953, A376954, A376955, A376956, A376957, A376958, A376959, A376960.

Programs

  • Mathematica
    a[n_] := Select[Range[200], (2n)^(2 #)/(2 #)! < 1 &, 1]
Flatten[Table[a[n], {n, 0, 200}]]

A376455 a(n) = least k such that n^(2k+1)/(2k+1)! < 1.

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 68, 69, 70, 72, 73, 74, 76, 77, 78, 80, 81, 83, 84, 85, 87, 88
Offset: 0

Views

Author

Clark Kimberling, Oct 17 2024

Keywords

Comments

The numbers n^(2k+1)/(2k+1)! are the coefficients in the Maclaurin series for sin x when x = 1. If m>a(n), then n^(2k+1)/(2k+1)! < 1.

Crossrefs

Cf. A370507, A376284, A376952, A376953, A376954, A376955, A376956, A376957, A376958, A376959, A376960.

Programs

  • Mathematica
    a[n_] := Select[Range[z], n^(2 # + 1)/(2 # + 1)! < 1 &, 1]
Flatten[Table[a[n], {n, 0, 100}]]
Showing 1-10 of 10 results.

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