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 A232716 #52 Feb 28 2023 23:48:49
%S A232716 7,3,0,7,0,8,0,8,4,2,4,8,1,4,3,0,9,8,3,4,5,4,5,9,3,8,9,9,7,0,9,9,0,1,
%T A232716 3,7,7,3,6,7,2,3,2,8,7,2,9,1,6,6,0,2,7,5,7,3,5,4,9,8,3,9,1,9,5,1,0,0,
%U A232716 7,2,9,3,2,5,3,5,5,1,3,5,4,0,2,6,0,1,4,0,8,2,9,3,5,0,7,6,2,1,1,9,6
%N A232716 Decimal expansion of the ratio of the length of the boundary of any parbelos to the length of the boundary of its associated arbelos: (sqrt(2) + log(1 + sqrt(2))) / Pi.
%C A232716 Same as decimal expansion of P/Pi, where P is the Universal parabolic constant (A103710). - _Jonathan Sondow_, Jan 19 2015
%C A232716 According to Wadim Zudilin, Campbell's formula (see below) follows from results of Borwein, Borwein, Glasser, Wan (2011): Take n=-2, s=1/4 in equations (4) and (20) to see that the formula is about evaluating K_{-2,1/4}. Take r=-1/2, s=1/4 in (76) to see that K_{-2,1/4} = cos(Pi/4)-K_{0,1/4}/16. Finally, use (51) and (52) to conclude that K_{0,1/4} = 2G_{1/4} = 2*log(1+sqrt(2)). - _Jonathan Sondow_, Sep 03 2016
%H A232716 G. C. Greubel, <a href="/A232716/b232716.txt">Table of n, a(n) for n = 0..10000</a>
%H A232716 D. Borwein, J. M. Borwein, M. L. Glasser, J. G. Wan, <a href="https://doi.org/10.1016/j.jmaa.2011.06.001">Moments of Ramanujan's generalized elliptic integrals and extensions of Catalan's constant</a>, J. Math. Anal. Appl., 384 (2) (2011), 478-496.
%H A232716 M. Hajja, <a href="https://zbmath.org/?q=an:1291.51018">Review Zbl 1291.51018</a>, zbMATH 2015.
%H A232716 M. Hajja, <a href="https://zbmath.org/?q=an:1291.51016">Review Zbl 1291.51016</a>, zbMATH 2015.
%H A232716 J. Sondow, <a href="http://arxiv.org/abs/1210.2279">The parbelos, a parabolic analog of the arbelos</a>, arXiv 2012, Amer. Math. Monthly, 120 (2013), 929-935.
%H A232716 E. Tsukerman, <a href="http://arxiv.org/abs/1210.5580">Solution of Sondow's problem: a synthetic proof of the tangency property of the parbelos</a>, arXiv:1210.5580 [math.MG], 2012-2013; Amer. Math. Monthly, 121 (2014), 438-443.
%F A232716 Equals A103710 / A000796.
%F A232716 Empirical: equals 3F2([-1/2,1/4,3/4],[1/2,1],1). - _John M. Campbell_, Aug 27 2016
%e A232716 0.730708084248143098345459389970990137736723287291660275735498...
%t A232716 RealDigits[(Sqrt[2] + Log[1 + Sqrt[2]])/Pi,10,100]
%o A232716 (PARI) (sqrt(2) + log(1 + sqrt(2)))/Pi \\ _G. C. Greubel_, Feb 02 2018
%o A232716 (Magma) R:= RealField(); (Sqrt(2) + Log(1 + Sqrt(2)))/Pi(R); // _G. C. Greubel_, Feb 02 2018
%Y A232716 Reciprocal of A232717. Ratio of areas is A177870.
%Y A232716 Cf. A000796, A103710.
%K A232716 nonn,cons,easy
%O A232716 0,1
%A A232716 _Jonathan Sondow_, Nov 28 2013