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A020773
Decimal expansion of 1/4.
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
0,1
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)
FORMULA
1/4 = Sum_{n >= 1} (-1)^(n+1)*n/(4*n^2-1). - Bruno Berselli, Sep 09 2020
MATHEMATICA
RealDigits[1/4, 10, 100][[1]] (* Alonso del Arte, Jun 05 2016 *)
PROG
(PARI) .25 \\ Charles R Greathouse IV, Apr 15 2015
CROSSREFS
Sequence in context: A252783 A192225 A020821 * A249422 A100085 A159986
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved