A020773 - OEIS

A020773

Decimal expansion of 1/4.

2, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

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OFFSET

0,1

COMMENTS

In the complex plane, this purely real number gives the coordinates for the inward cusp of the main cardioid of the Mandelbrot set. - Alonso del Arte, Jun 05 2016

Equals the sum of the fractional parts of the odd-indexed zeta values [Adamchik]: Sum_{k>=1} [zeta(2k+1)-1] = 1/4 = A002117-1 + A013663-1 + A013665-1 + ... - R. J. Mathar, Jan 13 2021

The probability that the center of a disk (or a square) lies within the triangle formed by three points chosen uniformly and independently at random from the interior of that disk (or that square). - Amiram Eldar, Feb 14 2026

The asymptotic probability that the greatest common divisor of two positive integers selected independently at random is an even number. - Amiram Eldar, Feb 24 2026

The probability that a chord defined by a midpoint chosen uniformly at random in the interior of a circle is longer than a side of an equilateral triangle inscribed in this circle (the third solution of Bertrand's problem, 1889). - Amiram Eldar, Apr 18 2026

LINKS

Table of n, a(n) for n=0..98.

Victor S. Adamchik and H. M. Srivastava, Some series of the zeta and related functions, Analysis (Munich) 18 (1998), 271-288, eq (1.7).

Joseph Bertrand, Calcul des probabilités, Gauthier-Villars, Paris, 1889, pp. 5-6.

Index entries for linear recurrences with constant coefficients, signature (1).

FORMULA

Equals (1/2) * Integral_{x>=0} 1/cosh(Pi*x) dx. - Bruno Berselli, Mar 20 2013

Equals Sum_{n >= 1} (-1)^(n+1)*n/(4*n^2-1). - Bruno Berselli, Sep 09 2020

EXAMPLE

0.25000000000000000000...

MATHEMATICA

RealDigits[1/4, 10, 100][[1]] (* Alonso del Arte, Jun 05 2016 *)