A384682 Decimal expansion of (5/6)*phi = 5*(1 + sqrt(5))/12, where phi is the golden ratio.

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

Offset: 1

Author

Kritsada Moomuang, Jun 06 2025

Keywords

• nonn
• cons
• easy

Examples

			1.34836165729157904017...
		

Crossrefs

Cf. A001622, A021016, A134944, A134946, A384238.

Programs

Mathematica

RealDigits[GoldenRatio * 5/6, 10, 100, 0][[1]]

Formula

Minimal polynomial: 36*x^2 - 30*x - 25.

Equals Integral_{x=0..1} sqrt(x + sqrt(x + sqrt(x + ...))) dx.

Equals Integral_{x=0..1} (1 + sqrt(1 + 4*x))/2 dx.

Equals 10*A134944/3 = 5*A134946. - Hugo Pfoertner, Jun 07 2025