The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A278386 Decimal expansion of the excess of the exponential curve arc length over the length of the x-axis from -infinity to zero. 2
 2, 2, 5, 9, 8, 7, 1, 5, 5, 9, 1, 3, 4, 9, 7, 3, 3, 2, 9, 8, 6, 3, 1, 1, 5, 2, 0, 6, 8, 8, 0, 8, 2, 3, 3, 7, 6, 1, 7, 0, 1, 1, 6, 8, 1, 4, 7, 5, 5, 6, 7, 9, 1, 6, 5, 4, 4, 0, 6, 4, 1, 3, 8, 8, 3, 0, 7, 4, 8, 9, 1, 6, 2, 0, 9, 7, 7, 5, 6, 6, 6, 6, 2, 2, 5, 4, 3, 9, 6, 9, 4, 1, 3, 8, 0, 4, 2, 1, 7, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Table of n, a(n) for n=0..99. Jean-François Alcover, Involute of the exponential curve (left branch). FORMULA Equals Integral_{-infinity..0} (sqrt(1 + exp(2x))-1) dx. Equals sqrt(2) - 1 + log(2) - log(1 + sqrt(2)). Equals sqrt(2) - 1 - arcsinh(7/(4*(5 + 3*sqrt(2)))). - Jan Mangaldan, Nov 23 2020 Equals sqrt(2) - 1 - arcsinh((5 - 3*sqrt(2))/4). - Vaclav Kotesovec, Nov 27 2020 EXAMPLE 0.22598715591349733298631152068808233761701168147556791654406413883... MATHEMATICA RealDigits[Sqrt[2] - 1 + Log[2] - Log[1 + Sqrt[2]], 10, 100][[1]] RealDigits[Sqrt[2] - 1 - ArcSinh[7/(4 (5 + 3 Sqrt[2]))], 10, 100][[1]] (* Jan Mangaldan, Nov 22 2020 *) PROG (PARI) sqrt(2) - 1 + log(2) - log(1 + sqrt(2)) \\ Michel Marcus, Nov 20 2016 CROSSREFS Cf. A222362 (a similar constant). Sequence in context: A233073 A275266 A223387 * A262614 A184296 A131133 Adjacent sequences: A278383 A278384 A278385 * A278387 A278388 A278389 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Nov 20 2016 STATUS approved

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

Last modified May 29 11:22 EDT 2024. Contains 372940 sequences. (Running on oeis4.)