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 1-6 of 6 results.

A376956 a(n) = least k such that n^(2k)/(2 k)! < 1.

Original entry on oeis.org

1, 1, 2, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 32, 33, 34, 36, 37, 38, 40, 41, 42, 44, 45, 46, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 71, 72, 74, 75, 76, 78, 79, 80, 82, 83, 84, 86, 87, 88
Offset: 0

Views

Author

Clark Kimberling, Oct 12 2024

Keywords

Comments

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

Crossrefs

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

Programs

  • Mathematica
    a[n_] := Select[Range[200], n^(2 #)/(2 #)! < 1 &, 1];
Flatten[Table[a[n], {n, 0, 200}]]
  • Python
    from itertools import count
from math import gcd
def A376956(n):
    a, b = 1, 1
    for k in count(1):
        a *= n**2
        b *= (m:=k<<1)*(m-1)
        if a < b: return k
        c = gcd(a,b)
        a, b = a//c, b//c # Chai Wah Wu, Oct 16 2024

Formula

a(n) ~ exp(1)*n/2 - 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}]]

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 1-6 of 6 results.

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