A387235 Decimal expansion of 2*log(2)/3.

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

Offset

0,1

Comments

Area enclosed by the curve of the equation x^6 + y^6 - x^3*y + x*y^3 = 0.

The asymptotic mean of A256232. - Amiram Eldar, Aug 23 2025

The probability that the centroid of an equilateral triangle is contained within the triangle formed by choosing one point uniformly and independently at random on each of its three sides (see Starvind link). - Amiram Eldar, Mar 03 2026

Links

Table of n, a(n) for n=0..99.

Michael I. Shamos, A catalog of the real numbers, (2007). See p. 436.

Starvind, Triangle Centroid Probability, Interesting Math Problems and Puzzles, 2021.

Index entries for transcendental numbers.

Formula

Equals A002162*A010722.

Equals log(4)/3 = A010701*A016627.

Equals Sum_{k>=0} (-1)^k/((3*k + 1)*(3*k + 2)) = Integral_{x=0..1} x^2*log(1 + 1/x^3) = -Integral_{x=0..1} log[1 - x^6]/x^4. [Shamos]

Equals A016627/3 = 2*A193535. - Hugo Pfoertner, Aug 23 2025

Example

0.46209812037329687294482141430545104538366675624...

Mathematica

RealDigits[2Log[2]/3, 10, 100][[1]]

Crossrefs

Cf. A002162, A001504, A010701, A010722, A016627, A193535, A256232.

Sequence in context: A016491 A347052 A375366 * A373635 A160327 A124259

Adjacent sequences: A387232 A387233 A387234 * A387236 A387237 A387238

Keyword

nonn,cons

Author

Stefano Spezia, Aug 23 2025

Status

approved