A069997 - OEIS

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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

(list; constant; graph; refs; listen; history; text; internal format)

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). [From Clark Kimberling, Oct 02 2011]

LINKS

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

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

CROSSREFS

Sequence in context: A155735 A153611 A068470 * A361059 A199373 A247037

Adjacent sequences: A069994 A069995 A069996 * A069998 A069999 A070000