A384682 -id:A384682 - cp's OEIS frontend

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

Kritsada Moomuang, May 22 2025

			0.75485615244018624891...

Cf. A002163, A002390, A384682

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

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.

A383659 Decimal expansion of phi + 2*log(phi), where phi is the golden ratio.

Original entry on oeis.org

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

Offset: 1

Kritsada Moomuang, Jun 11 2025

			2.58045763886910174320...

Cf. A001622, A002390, A202543, A384238, A384682.

RealDigits[GoldenRatio + 2 * Log[GoldenRatio], 10, 100, 0][[1]]

Equals Integral_{x=0..1} sqrt(1/x + sqrt(1/x + sqrt(1/x + ...))) dx.
Equals Integral_{x=0..1} (1 + sqrt(1 + 4/x))/2 dx.
Equals A001622 + A202543.

cp's OEIS Frontend

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

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