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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

Comments

Also, decimal expansion of 1/2 * integral_0^infinity 1/cosh(Pi*x) dx. - Bruno Berselli, Mar 20 2013

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

Links

• V. S. Adamchi and H. M. Srivastava, Some series of the zeta and related functions, Analysis (Munich) 18 (1998) 271-288, eq (1.7)
• Index entries for linear recurrences with constant coefficients, signature (1).

Programs

Mathematica

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

PARI

 25 \\ Charles R Greathouse IV, Apr 15 2015

Formula

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