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

1,2

Links

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

Index entries for algebraic numbers, degree 2.

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

Example

1.34836165729157904017...

Mathematica

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

Prog

(PARI) 5*(1 + sqrt(5))/12 \\ Charles R Greathouse IV, May 18 2026

Crossrefs

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

Sequence in context: A213922 A306568 A154743 * A020812 A021291 A179104

Adjacent sequences: A384679 A384680 A384681 * A384683 A384684 A384685

Keyword

nonn,cons,easy

Author

Kritsada Moomuang, Jun 06 2025

Status

approved