A069997 Decimal expansion of (negative of) root of exp(x)+sin(x)=0.

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

Offset

0,1

Comments

The number -0.588532... is the greatest negative root of e^x+sin(x), and 0.588532... is the least positive root of e^(-x)=sin(x). - Clark Kimberling, Oct 02 2011

Links

Table of n, a(n) for n=0..103.

Index entries for transcendental numbers.

Example

-0.5885327439818610774324520457029036885312715161090305333199142995116725533...

Mathematica

x /. FindRoot[ Exp[x] + Sin[x] == 0, {x, 0}, WorkingPrecision -> 110] // RealDigits[#, 10, 104]& // First (* Jean-François Alcover, Jun 18 2013 *)

Prog

(PARI) /* 300 significant digits : */ s=0; for(n=1, 250, s=s+sign(log(sin(s)^2)/2-s)/2^n; if(n>249, print1(s, ", ")))
(PARI) solve(x=0, 1, exp(-x)+sin(-x)) \\ Charles R Greathouse IV, Jun 18 2013
(PARI) -log(solve(y=.5, .99, real((y^I-y^-I)/I)/2+y)) \\ Charles R Greathouse IV, Feb 11 2025

Crossrefs

Sequence in context: A155735 A153611 A068470 * A361059 A199373 A247037

Adjacent sequences: A069994 A069995 A069996 * A069998 A069999 A070000

Keyword

cons,easy,nonn

Author

Benoit Cloitre, May 01 2002

Extensions

Digits beyond a(75) corrected by Jean-François Alcover, Jun 18 2013

Status

approved