The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A247719 Decimal expansion of Integral_{t=0..Pi/2} sqrt(tan(t)) dt. 10
 2, 2, 2, 1, 4, 4, 1, 4, 6, 9, 0, 7, 9, 1, 8, 3, 1, 2, 3, 5, 0, 7, 9, 4, 0, 4, 9, 5, 0, 3, 0, 3, 4, 6, 8, 4, 9, 3, 0, 7, 3, 1, 0, 8, 4, 4, 6, 8, 7, 8, 4, 5, 1, 1, 1, 5, 4, 2, 6, 9, 7, 8, 0, 3, 4, 7, 8, 2, 1, 7, 3, 9, 6, 5, 4, 9, 7, 3, 6, 9, 5, 5, 2, 8, 7, 6, 6, 3, 4, 6, 7, 3, 8, 2, 3, 8, 2, 6, 1, 8, 6, 8, 1, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 D. H. Bailey, J. M. Borwein, Highly Parallel, High-Precision Numerical Integration p. 7. (2005) Lawrence Berkeley National Laboratory. FORMULA Equals Pi/sqrt(2). Equals A063448/2. c = 2*( Sum_{k >= 0} (-1)^k/(4*k + 1) + Sum_{k >= 0} (-1)^k/(4*k + 3) ) = 2*(A181048 + A181049). - Peter Bala, Sep 21 2016 From Amiram Eldar, Aug 07 2020: (Start) Equals Integral_{x=0..Pi} 1/(cos(x)^2 + 1) dx = Integral_{x=0..Pi} 1/(sin(x)^2 + 1) dx. Equals Integral_{x=-oo..oo} 1/(x^4 + 1) dx. Equals Integral_{x=-oo..oo} x^2/(x^4 + 1) dx. Equals Integral_{x=0..oo} log(1 + 1/(2 * x^2)) dx. (End) EXAMPLE 2.22144146907918312350794049503034684930731... MATHEMATICA RealDigits[Pi/Sqrt[2], 10, 104] // First PROG (PARI) default(realprecision, 100); Pi/sqrt(2) \\ G. C. Greubel, Sep 07 2018 (MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)/Sqrt(2); // G. C. Greubel, Sep 07 2018 CROSSREFS Cf. A063448, A093954, A193887, A244976, A181048, A181049. Sequence in context: A105777 A014572 A071458 * A131308 A261360 A184242 Adjacent sequences:  A247716 A247717 A247718 * A247720 A247721 A247722 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Sep 23 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 15:34 EST 2021. Contains 349463 sequences. (Running on oeis4.)