A196825 - OEIS

%I #15 May 03 2024 19:52:05

%S 7,1,9,4,2,1,2,9,6,3,2,7,4,1,0,3,1,5,7,1,6,9,2,2,9,7,0,0,3,7,3,3,2,0,

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

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

%N Decimal expansion of the least x > 0 satisfying 1/(1 + x^2) = sin(x).

%H G. C. Greubel, <a href="/A196825/b196825.txt">Table of n, a(n) for n = 0..10000</a>

%e 0.7194212963274103157169229700373320490851010...

%t Plot[{1/(1 + x^2), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, 2}]

%t t = x /. FindRoot[1 == (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t]  (* A196825 *)

%t t = x /. FindRoot[1 == 2 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t]  (* A196826 *)

%t t = x /. FindRoot[1 == 3 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t]  (* A196827 *)

%t t = x /. FindRoot[1 == 4 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t]  (* A196828 *)

%t t = x /. FindRoot[1 == 5 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t]  (* A196829 *)

%t t = x /. FindRoot[1 == 6 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t]  (* A196830 *)

%o (PARI) a=1; c=1; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018

%Y Cf. A196832.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 07 2011