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A020773 Decimal expansion of 1/4. 4

%I #22 Jan 13 2021 08:12:15

%S 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,

%T 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,

%U 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

%N Decimal expansion of 1/4.

%C Also, decimal expansion of 1/2 * integral_0^infinity 1/cosh(Pi*x) dx. - _Bruno Berselli_, Mar 20 2013

%C 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

%C 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

%H V. S. Adamchi and H. M. Srivastava, <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.9800">Some series of the zeta and related functions</a>, Analysis (Munich) 18 (1998) 271-288, eq (1.7)

%F 1/4 = Sum_{n >= 1} (-1)^(n+1)*n/(4*n^2-1). - _Bruno Berselli_, Sep 09 2020

%t RealDigits[1/4, 10, 100][[1]] (* _Alonso del Arte_, Jun 05 2016 *)

%o (PARI) .25 \\ _Charles R Greathouse IV_, Apr 15 2015

%K nonn,cons,easy

%O 0,1

%A _N. J. A. Sloane_.

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)