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 21-24 of 24 results.

A371604 Decimal expansion of 5 * sqrt(3 - phi) / (2 * Pi).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Apr 01 2024

Keywords

Examples

			0.93548928378863903321291906615298281...

Crossrefs

Cf. A019845, A060294, A086089, A089491, A094874, A112628, A182007, A258403.

Programs

  • Mathematica
    RealDigits[5 Sqrt[3 - GoldenRatio]/(2 Pi), 10, 99][[1]]

Formula

Equals Product_{k>=1} (1 - 1/(5*k)^2).
Equals A258403/Pi. - Hugo Pfoertner, Apr 01 2024

A385448 Decimal expansion of sqrt(5 + 7*phi)/sqrt(11), with the golden section phi = A001622.

Original entry on oeis.org

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

Views

Author

Wolfdieter Lang, Jul 01 2025

Keywords

Comments

This equals the ratio length(Z, D_1)/s, with the fixed point of a complex loxodromic map w mapping iteratively golden triangles, starting with the one inscribed in a circumcircle with center ot the origin of the complex plane, the top vertex D_1 = i (the complex unit) and the base D_2 = (s - phi*i)/2, D_3 = (-s - phi*i)/2, with s = A182007.
See A385445 for details and a linked paper.

Examples

			1.218278887359662291535460267917274745203687400531554...

Crossrefs

Cf. A001622, A182007, A010468, A385445.

Programs

  • Mathematica
    RealDigits[Sqrt[(5 + 7*GoldenRatio)/11], 10, 120][[1]] (* Amiram Eldar, Jul 02 2025 *)

Formula

Equals sqrt(5 + 7*phi)/sqrt(11) = sqrt(5 + 7*phi)/A010468.
Equals A385447/(A010468*A182007).

A296183 Decimal expansion of (1/2)*sqrt(7 + phi), with the golden section from A001622.

Original entry on oeis.org

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

Views

Author

Wolfdieter Lang, Jan 08 2018

Keywords

Comments

In a regular pentagon inscribed in a unit circle this equals the second largest distance between a vertex and a midpoint of a side. The shortest such distance is (1/2)*sqrt(3 - phi) = (1/2)*A182007 = 0.58778525229..., and the longest 1 + phi/2 = (1/2)*(2 + phi) = (1/2)*A296184 = 1.80901699437...

Examples

			1.467824409521613628098163726467121337542565559888420020510299297523294383...

Crossrefs

Cf. A001622, A182007, A296184.

Programs

  • Mathematica
    First@ RealDigits[Sqrt[7 + GoldenRatio]/2, 10, 98] (* Michael De Vlieger, Jan 13 2018 *)

Formula

(1/2)*sqrt(7 + phi). From the comment on the pentagon above this results from sqrt((5/4)^2 + (sqrt(3 - phi)/2 + sqrt(7 - 4*phi)/4)^2).

A358938 Decimal expansion of the real root of 2*x^5 - 1.

Original entry on oeis.org

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

Views

Author

Wolfdieter Lang, Dec 07 2022

Keywords

Comments

This is the reciprocal of A005531.
The other two complex conjugate pairs of roots are obtained, with the present number r = (1/2)^(1/5) and the golden section phi (A001622), from x1 = r*exp(Pi*i*2/5) = r*(phi - 1 + sqrt(2 + phi)*i)/2 = r*(A001622 - 1 + A188593*i)/2 = 0.2690149185... + 0.8279427859...*i, x2 = r*exp(Pi*i*4/5) = r*(-phi + sqrt(3 - phi)*i)/2 = r*(-A001622 + A182007*i)/2 = -0.7042902001... + 0.5116967824...*i.

Examples

			0.87055056329612413913627001747974609897912542434800304824185956850675...

Crossrefs

Cf. A001622, A182007, A188593, A005531, A011101.

Programs

  • Mathematica
    RealDigits[Surd[1/2, 5], 10, 120][[1]] (* Amiram Eldar, Dec 07 2022 *)

Formula

r = (1/2)^(1/5) = 1/A005531.
Equals A011101/2. - Hugo Pfoertner, Mar 24 2025
Previous Showing 21-24 of 24 results.

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

Content is available under The OEIS End-User License Agreement.