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 1-3 of 3 results.

A308717 Decimal expansion of cosh(sqrt(3)*Pi/2)*sech(Pi/2).

Original entry on oeis.org

3, 0, 4, 0, 1, 9, 1, 5, 5, 1, 6, 4, 2, 5, 5, 3, 0, 7, 5, 6, 0, 1, 8, 6, 0, 0, 2, 7, 9, 0, 0, 7, 5, 7, 2, 3, 3, 8, 2, 3, 8, 5, 4, 9, 0, 5, 8, 7, 9, 1, 7, 1, 6, 7, 7, 9, 4, 1, 6, 5, 9, 7, 5, 1, 8, 4, 0, 8, 8, 5, 3, 9, 2, 5, 2, 3, 3, 2, 0, 4, 4, 1, 9, 6, 5, 1, 4, 6, 1, 8, 2, 9, 9, 0, 2, 5, 5, 0, 2, 1, 9, 7, 1, 1, 2, 0, 4, 8, 3, 0, 3, 9, 2, 2, 3, 1, 0, 5, 0, 6
Offset: 1

Views

Author

Ilya Gutkovskiy, Jun 19 2019

Keywords

Examples

			3.040191551642553075601860027900757233823854905879...

Links

Crossrefs

Cf. A001844, A156648, A308642, A308718.

Programs

  • Mathematica
    RealDigits[Cosh[Sqrt[3] Pi/2] Sech[Pi/2], 10, 120][[1]]
  • PARI
    cosh(sqrt(3)*Pi/2)/cosh(Pi/2) \\ Michel Marcus, Jun 20 2019

Formula

Equals Product_{k>=0} (1 + 1/(2*k*(k + 1) + 1)).
Equals Product_{k>=0} (1 + 1/A001844(k)).

A330864 Decimal expansion of sinh(Pi/2)/2.

Original entry on oeis.org

1, 1, 5, 0, 6, 4, 9, 4, 5, 1, 1, 5, 3, 6, 4, 7, 4, 3, 6, 7, 3, 1, 5, 2, 0, 0, 1, 1, 7, 1, 7, 2, 1, 3, 5, 8, 9, 0, 8, 9, 0, 7, 3, 2, 5, 8, 2, 5, 8, 1, 9, 1, 3, 3, 2, 9, 8, 6, 4, 1, 9, 9, 0, 1, 5, 4, 6, 7, 8, 3, 0, 0, 6, 9, 0, 1, 5, 2, 4, 9, 9, 9, 2, 4, 0, 0, 2, 6, 1, 2, 2, 1, 7, 9, 6, 1, 4, 3, 2, 9, 8, 2, 9, 1, 9, 0, 1, 1, 2, 3
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 28 2020

Keywords

Comments

This constant is transcendental.

Examples

			(1 + 1/2^2) * (1 - 1/3^2) * (1 + 1/4^2) * (1 - 1/5^2) * (1 + 1/6^2) * ... = (e^(Pi/2) - e^(-Pi/2))/4 = 1.15064945115364743673152001...

Links

Crossrefs

Cf. A042972, A049006, A090986, A156648, A175615, A308715, A308716, A308718, A323983, A330865, A334401.

Programs

  • Mathematica
    RealDigits[Sinh[Pi/2]/2, 10, 110] [[1]]
  • PARI
    sinh(Pi/2)/2 \\ Michel Marcus, Apr 28 2020

Formula

Equals Sum_{k>=1} Pi^(2*k-1)/(4^k*(2*k-1)!).
Equals Product_{k>=2} (1 + (-1)^k/k^2).
Equals (i^(-i) - i^i)/4, where i is the imaginary unit.

A330865 Decimal expansion of cosh(Pi/2)/Pi.

Original entry on oeis.org

7, 9, 8, 6, 9, 6, 3, 1, 5, 9, 5, 6, 4, 6, 3, 0, 8, 4, 8, 6, 3, 8, 0, 6, 7, 0, 4, 2, 2, 1, 0, 9, 6, 1, 3, 8, 6, 9, 1, 4, 9, 2, 8, 7, 4, 1, 8, 5, 1, 2, 9, 1, 2, 3, 4, 8, 3, 7, 2, 6, 6, 4, 0, 6, 4, 5, 9, 0, 2, 4, 3, 1, 1, 2, 9, 6, 8, 6, 5, 4, 3, 0, 6, 7, 6, 6, 4, 1, 0, 6, 5, 9, 8, 7, 3, 9, 6, 2, 3, 2, 2, 2, 5, 7, 1, 0, 1, 5, 8, 5
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 28 2020

Keywords

Examples

			(1 - 1/2^2) * (1 + 1/3^2) * (1 - 1/4^2) * (1 + 1/5^2) * (1 - 1/6^2) * ... = (e^(Pi/2) + e^(-Pi/2))/(2*Pi) = 0.7986963159564630848638067...

Crossrefs

Cf. A042972, A049006, A049541, A156648, A175615, A308715, A308716, A308718, A323982, A330864, A334402.

Programs

  • Mathematica
    RealDigits[Cosh[Pi/2]/Pi, 10, 110] [[1]]
  • PARI
    cosh(Pi/2)/Pi \\ Michel Marcus, Apr 28 2020

Formula

Equals Sum_{k>=0} Pi^(2*k-1)/(4^k*(2*k)!).
Equals Product_{k>=2} (1 - (-1)^k/k^2).
Equals (i^(-i) + i^i)/(2*Pi), where i is the imaginary unit.
Showing 1-3 of 3 results.

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