A069997 - OEIS

%I #13 Jun 18 2013 10:18:47

%S 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,

%T 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,

%U 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

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

%C 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]

%e -0.5885327439818610774324520457029036885312715161090305333199142995116725533...

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

%o (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,",")))

%o (PARI) solve(x=0,1,exp(-x)+sin(-x)) \\ _Charles R Greathouse IV_, Jun 18 2013

%K cons,easy,nonn

%O 0,1

%A _Benoit Cloitre_, May 01 2002

%E Digits beyond a(75) corrected by _Jean-François Alcover_, Jun 18 2013