A384238 Decimal expansion of sqrt(5) - log(phi) - 1, where phi is the golden ratio.

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

Offset

0,1

Links

Table of n, a(n) for n=0..86.

Formula

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

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

Equals A002163 - A002390 - 1.

Example

0.75485615244018624891...

Mathematica

RealDigits[Sqrt[5] - Log[GoldenRatio] - 1, 10, 100, -1][[1]]

Crossrefs

Cf. A002163, A002390, A384682

Sequence in context: A289032 A289005 A225408 * A109134 A075778 A289033

Adjacent sequences: A384235 A384236 A384237 * A384239 A384240 A384241

Keyword

nonn,cons

Author

Kritsada Moomuang, May 22 2025

Status

approved