A091651 -id:A091651 - cp's OEIS frontend

A385647 Decimal expansion of 1 - log(2)/2.

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

Offset: 0

Paolo Xausa, Jul 06 2025

Probability that floor(x/y) is even for x, y chosen randomly in (0,1).

			0.65342640972002734529138393927091171596224993281987...

Paolo Xausa, Table of n, a(n) for n = 0..10000
Morphocular, The answer involves Pi because why wouldn't it?, YouTube video, 2025 (see second half of video).

Cf. A002162, A091651.

Essentially the same as A382854.

SetDefaultRealField(RealField(100)); [1 - Log(2)/2]; // Vincenzo Librandi, Jul 07 2025

First[RealDigits[1 - Log[2]/2, 10, 100]]

Equals 1 - A002162/2.

A210958 Decimal expansion of 1 - (Pi/4).

Original entry on oeis.org

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

Offset: 0

Omar E. Pol, Aug 02 2012

Decimal expansion of (4 - Pi)/4.
Area between a square and the inscribed quarter circle of radius 1.
Also area between a circle of radius 1 and the circumscribed square, divided by 4.
Also area between a circle of diameter 1 and the circumscribed square. - Omar E. Pol, Sep 24 2013
Also volume between a cube of side length 1 and the inscribed cylinder. - Omar E. Pol, Sep 25 2013

			0.21460183660255169038433915418012427895070765015622...

M. L. Glasser, A note on Beukers's and related integrals, Amer. Math. Monthly 126(4) (2019), 361-363.
Index entries for transcendental numbers

Cf. A003881, A153799.

Essentially the same as A091651.

RealDigits[1 - Pi/4, 10, 87][[1]] (* Bruno Berselli, Aug 03 2012 *)

1-Pi/4 \\ Charles R Greathouse IV, Oct 01 2022

1 - (Pi/4) = (4 - Pi)/4 = 1 - A003881 = A153799/4.
From Amiram Eldar, Jun 29 2020: (Start)
Equals Sum_{k>=0} (-1)^k/(2*k+3).
Equals Integral_{x=0..Pi/4} tan(x)^2 dx.
Equals Integral_{x=0..1} arcsin(x) dx /(1+x)^2.
Equals Integral_{x=1..oo} dx/(x^2+x^4). (End)
Equals -Integral_{x=0..1, y=0..1} arcsin(x*y)/((1+x*y)^2*log(x*y)) dx dy. (Apply Theorem 1 or Theorem 2 from Glasser (2019) to one of Amiram Eldar's integrals.) - Petros Hadjicostas, Jun 29 2020
Continued fraction 1/(3 + 3^2/(2 + 5^2/(2 + 7^2/(2 + ... )))). - Peter Bala, Feb 28 2024

More terms from David Scambler, Aug 02 2012

cp's OEIS Frontend

A385647 Decimal expansion of 1 - log(2)/2.

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