A356869 Decimal expansion of 4 / sqrt(5).

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

Offset

1,2

Comments

The area of a golden rectangle inscribed in a unit circle.

The width and height of the rectangle are:

W = sqrt(2 - 2 / sqrt(5)) = A179290.

H = sqrt(2 + 2 / sqrt(5)) = A121570.

Links

Table of n, a(n) for n=1..97.

Formula

Equals [1; 1, 3, 1, 2] (periodic continued fraction expansion). - Peter Luschny, Sep 02 2022

Equals 1/A204188. - Alois P. Heinz, Sep 02 2022

Example

1.7888543819998317...

Maple

parse(substring(convert(evalf(4 / sqrt(5), 105), string), 1..98));

Mathematica

RealDigits[4 / Sqrt[5], 10, 105][[1]][[Range[1, 97]]]

Prog

(MATLAB) cell2mat(struct2cell(struct(vpa(4 / sqrt(5), 105)))); ans(1:98)

Crossrefs

Cf. A121570, A179290, A204188.

Sequence in context: A248224 A092290 A156571 * A099987 A226320 A021563

Adjacent sequences: A356866 A356867 A356868 * A356870 A356871 A356872

Keyword

nonn,cons,easy

Author

Michal Paulovic, Sep 01 2022

Status

approved