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!)
 A196504 Decimal expansion of the least x > 0 satisfying x + tan(x) = 0. 11
 2, 0, 2, 8, 7, 5, 7, 8, 3, 8, 1, 1, 0, 4, 3, 4, 2, 2, 3, 5, 7, 6, 9, 7, 1, 1, 2, 4, 7, 3, 4, 7, 1, 4, 3, 7, 6, 1, 0, 8, 3, 8, 0, 0, 2, 8, 7, 5, 9, 3, 9, 4, 0, 8, 8, 8, 1, 7, 1, 6, 6, 0, 7, 4, 4, 4, 9, 8, 6, 6, 5, 0, 3, 1, 0, 4, 2, 7, 6, 2, 3, 4, 5, 9, 2, 2, 7, 9, 5, 1, 5, 0, 4, 2, 5, 6, 3, 0, 6, 3, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let L be the least x > 0 satisfying x + tan(x) = 0. Then L is also the least x > 0 satisfying x = (sin(x))(sqrt(1+x^2)). Consequently, for 0 < x < L, for all p > 0, 1/sqrt(1+x^2) - 1/x^p < sin(x) < 1/sqrt(1+x^2) for 0 < x < L. See A196500-A196503 and A196505 for related constants and inequalities. The number L also occurs in connection with Du Bois Reymond's constants; see the Finch reference. For x = L the area of right triangle with vertices (0,0), (x,0) and (x,sin(x)), i.e., the one inscribed into the half-wave curve, is maximal. - Roman Witula, Feb 05 2015 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, page 239. LINKS EXAMPLE L = 2.02875783811043422357697112473471437610838002... 1/L = 0.4929124517549075741877801898222329769156970132... MATHEMATICA Plot[{Sin[x], x/Sqrt[1 + x^2]}, {x, 0, 9}] t = x /.FindRoot[Sin[x] == x/Sqrt[1 + x^2], {x, .10, 3}, WorkingPrecision -> 100] RealDigits[t]   (* A196504 *) 1/t RealDigits[1/t] (* A196505 *) CROSSREFS Cf. A196505, A196500, A196502. Sequence in context: A021497 A201735 A029593 * A182550 A004514 A278748 Adjacent sequences:  A196501 A196502 A196503 * A196505 A196506 A196507 KEYWORD nonn,cons AUTHOR Clark Kimberling, Oct 03 2011 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 7 15:24 EST 2021. Contains 349581 sequences. (Running on oeis4.)