This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A193887 #41 Feb 08 2025 09:01:17
%S A193887 5,5,5,3,6,0,3,6,7,2,6,9,7,9,5,7,8,0,8,7,6,9,8,5,1,2,3,7,5,7,5,8,6,7,
%T A193887 1,2,3,2,6,8,2,7,7,1,1,1,7,1,9,6,1,2,7,7,8,8,5,6,7,4,4,5,0,8,6,9,5,5,
%U A193887 4,3,4,9,1,3,7,4
%N A193887 Decimal expansion of Pi * sqrt(2)/8.
%C A193887 This number arises as an addend in one way of giving the closed form of sum(k>=0, (-1)^k/(4*k + 1) ), for example, in Spiegel et al. (2009).
%D A193887 Murray R. Spiegel, Seymour Lipschutz, John Liu. Mathematical Handbook of Formulas and Tables, 3rd Ed. Schaum's Outline Series. New York: McGraw-Hill (2009): p. 135, equation 21.17
%H A193887 G. C. Greubel, <a href="/A193887/b193887.txt">Table of n, a(n) for n = 0..10000</a>
%H A193887 Piotr Garbaczewski and Vladimir A. Stephanovich, <a href="http://arxiv.org/abs/1106.1530">Semigroup modeling of confined Levy flights</a>, arXiv:1106.1530 [cond-mat.stat-mech], 2011, p. 8, equation 40.
%H A193887 Piotr Garbaczewski and Vladimir A. Stephanovich, <a href="https://doi.org/10.5506/APhysPolB.43.977">Dynamics of Confined Lévy Flights in Terms of (Lévy) Semigroups</a>, Acta Phys. Pol. B 43, 977-999 (2012). See p. 992.
%H A193887 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A193887 Equals Pi/(4*sqrt(2)).
%F A193887 Equals Sum_{k >= 0} (-1)^k * (4*k + 2)/((4*k + 1)*(4*k + 3)). - _Peter Bala_, Sep 21 2016
%F A193887 From _Amiram Eldar_, Aug 15 2020: (Start)
%F A193887 Equals Integral_{x=0..oo} 1/(x^2 + 8) dx.
%F A193887 Equals Integral_{x=0..oo} 1/(8*x^2 + 1) dx.
%F A193887 Equals Integral_{x=0..oo} 1/(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7) dx. (End)
%e A193887 0.55536036726979578088...
%t A193887 RealDigits[(Pi Sqrt[2])/8, 10, 100][[1]]
%o A193887 (PARI) Pi*sqrt(2)/8 \\ _G. C. Greubel_, Feb 02 2018
%o A193887 (Magma) R:= RealField(); Pi(R)*Sqrt(2)/8; // _G. C. Greubel_, Feb 02 2018
%Y A193887 Cf. A181048, A063448, A247719, A093954, A244976.
%K A193887 nonn,cons
%O A193887 0,1
%A A193887 _Alonso del Arte_, Aug 07 2011