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%I A020773 #26 Aug 06 2024 07:17:37
%S A020773 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 A020773 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 A020773 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 A020773 Decimal expansion of 1/4.
%C A020773 Also, decimal expansion of  1/2 * integral_0^infinity 1/cosh(Pi*x) dx. - _Bruno Berselli_, Mar 20 2013
%C A020773 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 A020773 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 A020773 V. S. Adamchi and H. M. Srivastava, <a href="https://citeseerx.ist.psu.edu/pdf/b75ac68b32e8225460584eb7c6c00bb6214b3f51">Some series of the zeta and related functions</a>, Analysis (Munich) 18 (1998) 271-288, eq (1.7)
%H A020773 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A020773 1/4 = Sum_{n >= 1} (-1)^(n+1)*n/(4*n^2-1). - _Bruno Berselli_, Sep 09 2020
%t A020773 RealDigits[1/4, 10, 100][[1]] (* _Alonso del Arte_, Jun 05 2016 *)
%o A020773 (PARI) .25 \\ _Charles R Greathouse IV_, Apr 15 2015
%K A020773 nonn,cons,easy
%O A020773 0,1
%A A020773 _N. J. A. Sloane_.

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