A359532 Decimal expansion of 2*log(2)/Pi.

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

Offset

0,1

Comments

2*log(2)*n/Pi is also the dominant term in the asymptotic expansion of Sum_{k=1..n-1} (-1)^(k+1)*csc(Pi*k/n) at n tending to infinity. - Iaroslav V. Blagouchine, Apr 10 2025

The probability that a straight line drawn through a point uniformly selected at random in the interior of a square, with a direction independently and uniformly selected at random, intersects two adjacent sides. - Amiram Eldar, Apr 07 2026

Links

Table of n, a(n) for n=0..97.

Iaroslav V. Blagouchine, On a Generalization of Watson's Trigonometric Sum (On Dowker's Sum of Order One Half), INTEGERS, Electronic Journal of Combinatorial Number Theory, vol. 25, Article #A30, pp. 1-33, 2025. See p. 18.

John M. Campbell, Applications of a class of transformations of complex sequences, arXiv:2212.13305 [math.NT], 2022. See pp. 2, 8.

Formula

Equals A016627/A000796.

Equals A002162*A060294.

Equals 2*A284983.

Equals Sum_{i>=0} (-1/64)^i*binomial(2*i, i)^3*(4*i + 1)*H_{2*i}, where H_m is the m-th harmonic number (negated).

Equals log(A117191). - Amiram Eldar, Apr 07 2026

Example

0.441271200305303186792912864235995381965...

Mathematica

First[RealDigits[N[2Log[2]/Pi, 98]]]

Crossrefs

Cf. A000796, A001008, A002162, A002805, A002897, A016627, A016813, A060294, A117191.

Cf. A359533.

Sequence in context: A089746 A225330 A094884 * A281540 A053216 A325489

Adjacent sequences: A359529 A359530 A359531 * A359533 A359534 A359535

Keyword

nonn,cons

Author

Stefano Spezia, Jan 04 2023

Status

approved