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 A180434 Decimal expansion of constant (2 - Pi/2). 10
 4, 2, 9, 2, 0, 3, 6, 7, 3, 2, 0, 5, 1, 0, 3, 3, 8, 0, 7, 6, 8, 6, 7, 8, 3, 0, 8, 3, 6, 0, 2, 4, 8, 5, 5, 7, 9, 0, 1, 4, 1, 5, 3, 0, 0, 3, 1, 2, 4, 4, 7, 0, 8, 9, 5, 1, 2, 5, 2, 7, 7, 0, 3, 8, 4, 6, 0, 9, 1, 7, 9, 6, 8, 5, 6, 8, 9, 5, 5, 0, 0, 6, 8, 5, 9, 8, 2, 5, 8, 7, 3, 2, 8, 9, 4, 1, 4, 6, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS (2-Pi/2)*a^2 is the area of the loop of the right strophoid (also called the Newton strophoid) whose polar equation is r = a*cos(2*t)/cos(t) and whose Cartesian equation is x*(x^2+y^2) = a*(x^2-y^2) or y = +- x*sqrt((a-x)/(a+x)). See the curve with its loop at the Mathcurve link; the loop appears for -Pi/4 <= t <= Pi/4. - Bernard Schott, Jan 28 2020 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Robert FerrÃ©ol, Right strophoid, Math Curve. Nikita Kalinin and Mikhail Shkolnikov, The number Pi and summation by SL(2,Z), arXiv:1701.07584 [math.NT], 2016. Gives a formula. FORMULA Equals Integral_{t=0..Pi/4} ((cos(2*t))/cos(t))^2 dt. - Bernard Schott, Jan 28 2020 From Amiram Eldar, May 30 2021: (Start) Equals Sum_{k>=1} 2^k/(binomial(2*k,k)*k*(2*k + 1)). Equals Integral_{x=0..1} arcsin(x)*arccos(x) dx. (End) EXAMPLE 0.42920367320510338076867830836024855790141530... MATHEMATICA RealDigits[2-Pi/2, 10, 120][[1]] (* Harvey P. Dale, Oct 12 2013 *) CROSSREFS Cf. A004601, A180433, A222362. Sequence in context: A201531 A021237 A115881 * A201574 A077809 A201281 Adjacent sequences:  A180431 A180432 A180433 * A180435 A180436 A180437 KEYWORD cons,easy,nonn AUTHOR Jonathan Vos Post, Sep 05 2010 EXTENSIONS Corrected by Carl R. White, Sep 09 2010 More terms from N. J. A. Sloane, Sep 23 2010 STATUS approved

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Last modified August 17 12:30 EDT 2022. Contains 356189 sequences. (Running on oeis4.)