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.

Previous Showing 11-15 of 15 results.

A019886 Decimal expansion of sine of 77 degrees.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Comments

Equals sin(77*Pi/180). - Wesley Ivan Hurt, Sep 01 2014
An algebraic number of degree 48 and denominator 2. - Charles R Greathouse IV, Nov 06 2017

Examples

			0.974370064785235228539694480088268833005120988944567944597972222...

Links

Programs

Formula

Equals A019875 * A019888 + A019820 * A019833 = A019879 * A019892 + A019816 * A019829. - R. J. Mathar, Jan 27 2021

A019834 Decimal expansion of sine of 25 degrees.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Comments

An algebraic number of degree 12 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

Links

Programs

Formula

Equals A019829 * A019894 + A019814 * A019879. - R. J. Mathar, Jan 27 2021

A343056 Decimal expansion of the real part of i^(1/16), or cos(Pi/32).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Apr 04 2021

Keywords

Examples

			0.9951847266721968862448369...

Links

Crossrefs

cos(Pi/m): A010503 (m=4), A019863 (m=5), A010527 (m=6), A073052 (m=7), A144981 (m=8), A019879 (m=9), A019881 (m=10), A019884 (m=12), A232735 (m=14), A019887 (m=15), A232737 (m=16), A210649 (m=17), A019889 (m=18), A019890 (m=20), A144982 (m=24), A019893 (m=30). this sequence (m=32), A019894 (m=36).

Programs

  • Magma
    R:= RealField(127); Cos(Pi(R)/32); // G. C. Greubel, Sep 30 2022
  • Mathematica
    RealDigits[Cos[Pi/32], 10, 100][[1]] (* Amiram Eldar, Apr 27 2021 *)
  • PARI
    real(I^(1/16))
  • PARI
    cos(Pi/32)
  • PARI
    sqrt(2+sqrt(2+sqrt(2+sqrt(2))))/2
  • SageMath
    numerical_approx(cos(pi/32), digits=122) # G. C. Greubel, Sep 30 2022

Formula

Equals (1/2) * sqrt(2+sqrt(2+sqrt(2+sqrt(2)))).
Satisfies 32768*x^16 -131072*x^14 +212992*x^12 -180224*x^10 +84480*x^8 -21504*x^6 +2688*x^4 -128*x^2 +1 = 0. - R. J. Mathar, Aug 29 2025
Equals 2F1(-1/16,1/16;1/2;1/2). - R. J. Mathar, Aug 31 2025

A359837 Decimal expansion of the unsigned ratio of similitude between an equilateral reference triangle and its first Morley triangle.

Original entry on oeis.org

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

Views

Author

Frank M Jackson, Jan 14 2023

Keywords

Comments

The first Morley triangle of any reference triangle is always equilateral. Therefore a reference equilateral triangle and its first Morley triangle will be in a homothetic relationship. This sequence is the real terms of a constant that is the ratio of similitude of the homothety. The constant is negative.
If an equilateral triangle has a side a, a circumradius R and a first Morley triangle with side a', then a = R*sqrt(3) and a' = 8*R*(sin(Pi/9))^3, so the ratio of similitude between the two triangles is a'/a = (8/sqrt(3)) * (sin(Pi/9))^3. - Bernard Schott, Feb 06 2023

Examples

			0.1847925309040953727013520475722037558709135597926517172356...

Links

Crossrefs

Cf. A019819, A019829, A019879, A020760.

Programs

  • Mathematica
    RealDigits[Sin[Pi/18]/Cos[Pi/9], 10, 100][[1]]
N[Solve[x^3 + 3*x^2 - 6*x + 1 == 0, {x}][[2]], 90]
  • PARI
    sin(Pi/18)/cos(Pi/9) \\ Michel Marcus, Jan 15 2023

Formula

Equals sin(Pi/18)/cos(Pi/9).
A root of x^3+3*x^2-6*x+1.
Equals A019819/A019879. - Michel Marcus, Jan 15 2023
Equals 8 * A020760 * A019829^3. - Bernard Schott, Feb 06 2023

A387447 Decimal expansion of cos(Pi/27).

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Aug 29 2025

Keywords

Examples

			0.99323835774194298855...

Links

Formula

Equals sin(25*Pi/54) = 2F1(-1/18,1/18;1/2;3/4).
Largest of the 9 real-valued roots of 512*x^9 -1152*x^7 +864*x^5 -240*x^3 +18*x -1 =0.
4*this^3 -3*this = A019879.
Previous Showing 11-15 of 15 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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