A384683 Decimal expansion of Sum_{i >= 1} 1/(3*i-1) - 1/(3*i).

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

Offset: 0

Author

Jason Bard, Jun 06 2025

Keywords

• nonn
• cons

Comments

Generalization of infinite sum generating A002162 (natural logarithm of 2). That sum is Sum_{i >= 1} 1/(k*i-1) - 1/(k*i), where k = 2. Here, we set k = 3.

Examples

			0.24700625029501853726527624218757023027640090422925...
		

Links

• Jason Bard, Table of n, a(n) for n = 0..9999
• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 291.
• Index entries for transcendental numbers.

Crossrefs

Cf. A002162, A007494, A152743, A156057, A294514, A381671.

Programs

Mathematica

RealDigits[1/2 * Log[3] - (Sqrt[3]/18) * Pi, 10, 1000][[1]]

PARI

log(3)/2 - Pi/(6*sqrt(3)) \\ Amiram Eldar, Jun 07 2025

Formula

Equals (1/2) * log(3) - sqrt(3) * Pi / 18.

Equals Sum_{i>=1} 1/A152743(i).

Equals A294514/3. - Hugo Pfoertner, Jun 07 2025