A300071 Decimal expansion of the member z of a triple (x, y, z) solving a certain historical system of three equations with positive y.

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

Offset: 1

Author

Wolfdieter Lang, Mar 02 2018

Keywords

• nonn
• cons
• easy

Comments

See A300071 for the system of equations and references and links.

The current triple is (x = 10*A248752, A300070, z = this entry).

The other real solution is (x = x2 = 10*A248750, y = y2 = A300072, z = z2 = A300073).

Examples

			z = 4.15941305496235781067514124261339594098593560984019812235273326302039...
z/5 = 0.831882610992471562135028248522679188197187121968039624470546652604...
		

Crossrefs

Cf. A001622, A248750, A248752, A300070, A300072, A300073.

Programs

Mathematica

RealDigits[5 (GoldenRatio - (GoldenRatio - 1) Sqrt[GoldenRatio]), 10, 100][[1]] (* Bruno Berselli, Mar 02 2018 *)

Formula

z = 5*(phi - (phi-1)*sqrt(phi)), with the golden section phi = (1 + sqrt(5))/2 = A001622.

z = 10 - 2*y + (1/50)*y^3, with y = A300070.