A388812 Decimal expansion of 3/5+1 / sqrt(5).

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

Offset

1,3

Comments

The ratio of the maximum area to the mean area of the orthogonal projection of a regular icosahedron (cf. A395729). - Amiram Eldar, May 05 2026

Links

Table of n, a(n) for n=1..87.

Simon Plouffe, Numbers in the base e^Pi, 2025.

Index entries for algebraic numbers, degree 02.

Formula

Empirical: Equals Sum_{k>=0} A228864(k) / exp(k*Pi).

Equals A180251/3 = 2*A229780. - Hugo Pfoertner, Sep 23 2025

From Amiram Eldar, May 05 2026: (Start)

Equals 2*phi^2/5, where phi is the golden ratio (A001622).

Minimal polynomial: 25*x^2 - 30*x + 4. (End)

Example

1.0472135954999579392818347337462552471...

Mathematica

RealDigits[3/5 + 1/Sqrt[5], 10 , 120][[1]] (* Amiram Eldar, Sep 23 2025 *)

Prog

(PARI) 3/5 + 1/sqrt(5)

Crossrefs

Cf. A001622, A180251, A228864, A229780, A340725, A340724, A340722, A395729.

Apart from leading digits the same as A176453, A134974 and A010476.

Sequence in context: A388934 A387545 A388800 * A139346 A133390 A201403

Adjacent sequences: A388809 A388810 A388811 * A388813 A388814 A388815

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved