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 1-4 of 4 results.

A195702 Decimal expansion of arccos(-sqrt(2/3)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 23 2011

Keywords

Examples

			arccos(-sqrt(2/3)) = 2.5261129449405...

Links

Crossrefs

Cf. A195701.

Programs

  • Magma
    [Arccos(-Sqrt(2/3))]; // G. C. Greubel, Nov 18 2017
  • Mathematica
    r = Sqrt[2/3];
N[ArcSin[r], 100]
RealDigits[%]  (* A195696 *)
N[ArcCos[r], 100]
RealDigits[%]  (* A195695 *)
N[ArcTan[r], 100]
RealDigits[%]  (* A195701 *)
N[ArcCos[-r], 100]
RealDigits[%]  (* A195702 *)
RealDigits[ArcCos[-Sqrt[(2/3)]],10,120][[1]] (* Harvey P. Dale, Jan 15 2013 *)
  • PARI
    acos(-sqrt(2/3)) \\ G. C. Greubel, Nov 18 2017

Formula

Equals Pi - arcsin(sqrt(1/3)) = Pi - arctan(sqrt(1/2)). - Amiram Eldar, Jul 10 2023

A195708 Decimal expansion of arccos(sqrt(2/5)) and of arcsin(sqrt(3/5)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 23 2011

Keywords

Examples

			0.886077123792...

Links

Crossrefs

Cf. A073000, A105199, A195701.

Programs

  • Magma
    [Arccos(Sqrt(2/5))]; // G. C. Greubel, Nov 18 2017
  • Mathematica
    r = Sqrt[1/5]; s = Sqrt[2/5];
N[ArcSin[r], 100]
RealDigits[%]  (* A073000 *)
N[ArcCos[r], 100]
RealDigits[%]  (* A105199 *)
N[ArcTan[r], 100]
RealDigits[%]  (* A188595 *)
N[ArcCos[-r], 100]
RealDigits[%]  (* A137218 *)
N[ArcSin[s], 100]
RealDigits[%]  (* A195701 *)
N[ArcCos[s], 100]
RealDigits[%]  (* A195708 *)
N[ArcTan[s], 100]
RealDigits[%]  (* A195709 *)
N[ArcCos[-s], 100]
RealDigits[%]  (* A195710 *)
  • PARI
    acos(sqrt(2/5)) \\ G. C. Greubel, Nov 18 2017

Formula

Equals arctan(sqrt(3/2)). - Amiram Eldar, Jul 04 2023

A195709 Decimal expansion of arctan(sqrt(2/5)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 23 2011

Keywords

Examples

			arctan(sqrt(2/5)) = 0.5639426413606...

Links

Crossrefs

Cf. A195708.

Programs

  • Magma
    [Arctan(Sqrt(2/5))]; // G. C. Greubel, Nov 18 2017
  • Mathematica
    r = Sqrt[1/5]; s = Sqrt[2/5];
N[ArcSin[r], 100]
RealDigits[%]  (* A073000 *)
N[ArcCos[r], 100]
RealDigits[%]  (* A105199 *)
N[ArcTan[r], 100]
RealDigits[%]  (* A188595 *)
N[ArcCos[-r], 100]
RealDigits[%]  (* A137218 *)
N[ArcSin[s], 100]
RealDigits[%]  (* A195701 *)
N[ArcCos[s], 100]
RealDigits[%]  (* A195708 *)
N[ArcTan[s], 100]
RealDigits[%]  (* A195709 *)
N[ArcCos[-s], 100]
RealDigits[%]  (* A195710 *)
  • PARI
    atan(sqrt(2/5)) \\ G. C. Greubel, Nov 18 2017

A195710 Decimal expansion of arccos(-sqrt(2/5)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 23 2011

Keywords

Examples

			arccos(-sqrt(2/5)) = 2.25551552979717...

Links

Crossrefs

Cf. A195708, A195701.

Programs

  • Magma
    [Arccos(-Sqrt(2/5))]; // G. C. Greubel, Nov 18 2017
  • Mathematica
    r = Sqrt[1/5]; s = Sqrt[2/5];
N[ArcSin[r], 100]
RealDigits[%]  (* A073000 *)
N[ArcCos[r], 100]
RealDigits[%]  (* A105199 *)
N[ArcTan[r], 100]
RealDigits[%]  (* A188595 *)
N[ArcCos[-r], 100]
RealDigits[%]  (* A137218 *)
N[ArcSin[s], 100]
RealDigits[%]  (* A195701 *)
N[ArcCos[s], 100]
RealDigits[%]  (* A195708 *)
N[ArcTan[s], 100]
RealDigits[%]  (* A195709 *)
N[ArcCos[-s], 100]
RealDigits[%]  (* A195710 *)
RealDigits[ArcCos[-Sqrt[(2/5)]],10,120][[1]] (* Harvey P. Dale, Apr 06 2023 *)
  • PARI
    acos(-sqrt(2/5)) \\ G. C. Greubel, Nov 18 2017

Formula

Equals Pi - arcsin(sqrt(3/5)) = Pi - arctan(sqrt(3/2)). - Amiram Eldar, Jul 08 2023
Showing 1-4 of 4 results.

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