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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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.

A339745 Decimal expansion of Product_{n>=2} (1 - n^(-10)).

Original entry on oeis.org

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

Views

Author

Vaclav Kotesovec, Dec 15 2020

Keywords

Examples

			0.99900544248098947527378453585422724586059097385364736908229...

Crossrefs

Cf. A109219, A175615, A175616, A175617, A175618, A175619.

Programs

  • Maple
    evalf((cosh(sqrt((5 - sqrt(5))/2)*Pi) + sin(sqrt(5)*Pi/2)) * (cosh(sqrt((5 + sqrt(5))/2)*Pi) - sin(sqrt(5)*Pi/2)) / (40*Pi^4), 100);
  • Mathematica
    RealDigits[(Cosh[Sqrt[(5 - Sqrt[5])/2]*Pi] + Sin[Sqrt[5]*Pi/2]) * (Cosh[Sqrt[(5 + Sqrt[5])/2]*Pi] - Sin[Sqrt[5]*Pi/2]) / (40*Pi^4), 10, 100][[1]]
  • PARI
    exp(suminf(j=1, (1 - zeta(10*j))/j))
  • PARI
    prodinf(n=2, 1-1/n^10) \\ Michel Marcus, Dec 15 2020

Formula

Equals (cosh(sqrt((5 - sqrt(5))/2)*Pi) + sin(sqrt(5)*Pi/2)) * (cosh(sqrt((5 + sqrt(5))/2)*Pi) - sin(sqrt(5)*Pi/2)) / (40*Pi^4).
Equals exp(Sum_{j>=1} (1 - zeta(10*j))/j).

A371219 Decimal expansion of Product_{k>=1} (1 - 1/(2*k+1)^4).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Mar 31 2024

Keywords

Examples

			0.98535208438722062330349111379064867712159256...

Crossrefs

Cf. A003881, A175615, A258870, A369880, A371465.

Programs

  • Mathematica
    RealDigits[(1/8) Pi Cosh[Pi/2], 10, 100][[1]]

Formula

Equals (1/8) * Pi * cosh(Pi/2).

A346745 Decimal expansion of Product_{k>=2} (1 - 1/k^12).

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Jul 31 2021

Keywords

Examples

			0.999753913921893256003448570641909727180...

Links

Crossrefs

Cf. A109219, A175615, A175616, A175617, A175618, A175619, A339745.

Programs

  • Maple
    evalf(sinh(Pi) * cosh(Pi*sqrt(3)/2)^2 * (cosh(Pi) - cos(Pi*sqrt(3))) / (24*Pi^5), 120); # Vaclav Kotesovec, Aug 01 2021
  • Mathematica
    RealDigits[Sinh[Pi]*Cosh[Pi*Sqrt[3]/2]^2*(Cosh[Pi] - Cos[Pi*Sqrt[3]])/(24*Pi^5), 10, 120][[1]] (* Amiram Eldar, Jun 12 2023 *)
  • PARI
    exp(suminf(j=1, (1 - zeta(12*j))/j)) \\ Vaclav Kotesovec, Aug 01 2021

Formula

Equals sinh(Pi) * cosh(Pi*sqrt(3)/2)^2 * (cosh(Pi) - cos(Pi*sqrt(3))) / (24*Pi^5).
Equals exp(Sum_{j>=1} (1 - zeta(12*j))/j). - Vaclav Kotesovec, Aug 01 2021
Previous Showing 11-14 of 14 results.

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