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

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

1,2

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...

Links

Table of n, a(n) for n=1..98.

Index entries for algebraic numbers, degree 4.

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).

Minimal polynomial: 16*x^4 - 60*x^2 + 55. - Amiram Eldar, Jun 07 2026

Example

1.467824409521613628098163726467121337542565559888420020510299297523294383...

Mathematica

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

Prog

(PARI) sqrt((sqrt(5)+1)/2+7)/2 \\ Charles R Greathouse IV, May 19 2026
(PARI) polrootsreal(16*x^4 - 60*x^2 + 55)[4] \\ Charles R Greathouse IV, May 19 2026

Crossrefs

Cf. A001622, A182007, A296184.

Sequence in context: A169788 A369802 A300707 * A021876 A261491 A005670

Adjacent sequences: A296180 A296181 A296182 * A296184 A296185 A296186

Keyword

nonn,cons,easy

Author

Wolfdieter Lang, Jan 08 2018

Status

approved