A117240 Decimal expansion of solution to problem #10 in the Trefethen challenge.

0, 0, 0, 0, 0, 0, 3, 8, 3, 7, 5, 8, 7, 9, 7, 9, 2, 5, 1, 2, 2, 6, 1, 0, 3, 4, 0, 7, 1, 3, 3, 1, 8, 6, 2, 0, 4, 8, 3, 9, 1, 0, 0, 7, 9, 3, 0, 0, 5, 5, 9, 4, 0, 7, 2, 5, 0, 9, 5, 6, 9, 0, 3, 0, 0, 2, 2, 7, 9, 9, 1, 7, 3, 4, 3, 6, 6, 0, 6, 8, 5, 2, 7, 4, 3, 2, 7, 6, 5, 0, 0, 8, 4, 2, 8, 4, 5, 6, 4, 7, 2, 6, 9, 9, 1, 0, 1, 5, 3, 5, 3

Offset

0,7

References

David H. Bailey, Jonathan M. Borwein, Neil J. Calkin, Roland Girgensohn, D. Russell Luke and Victor H. Moll, Experimental Mathematics in Action, Wellesley, MA, A K Peters, 2007, p. 48.

Links

Amiram Eldar, Table of n, a(n) for n = 0..10007 (from Folkmar Bornemann's solution)

Folkmar Bornemann, Short remarks on the solution of the SIAM 100-digit challenge, 2002.

Folkmar Bornemann, Hitting the Ends, a web page for the book The SIAM 100-Digit Challenge.

Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel, The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing, SIAM, Philadelphia, 2004.

Eric Weisstein's World of Mathematics, Hundred-Dollar, Hundred-Digit Challenge Problems.

Wikipedia, Hundred-dollar, Hundred-digit Challenge problems.

Formula

Equals (2*arccos(sqrt(ModularLambda(I/10))))/Pi.

Example

0.0000003837587979251226103...

Mathematica

Flatten[{0, 0, 0, 0, 0, 0, RealDigits[(2*ArcCos[Sqrt[ModularLambda[I/10]]])/Pi, 10, 100][[1]]}] (* Vaclav Kotesovec, Aug 15 2015 after Eric W. Weisstein *)
N[2/Pi * ArcSin[(3-2*Sqrt[2])^2 * (2+Sqrt[5])^2 * (Sqrt[10]-3)^2 * (5^(1/4)-Sqrt[2])^4], 100] (* Vaclav Kotesovec, Aug 15 2015 after Bornemann *)

Crossrefs

Cf. A117231, A117232, A117233, A117234, A117235, A117236, A117237, A117238, A117239.

Sequence in context: A333287 A360199 A360851 * A151857 A359200 A125025

Adjacent sequences: A117237 A117238 A117239 * A117241 A117242 A117243

Keyword

nonn,cons

Author

Eric W. Weisstein, Mar 05 2006

Status

approved