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A196754 Decimal expansion of the least x>0 satisfying 1=3x*sin(x).

%I A196754 #8 Feb 11 2025 13:33:49
%S A196754 5,9,4,8,3,9,1,7,2,5,0,5,4,9,2,9,5,4,8,3,4,8,9,9,7,7,5,3,7,7,9,2,1,5,
%T A196754 1,0,8,5,6,7,7,7,0,5,1,7,4,0,1,9,0,8,8,9,2,4,7,6,3,0,9,2,7,7,9,1,2,3,
%U A196754 8,3,7,6,1,7,3,2,0,2,4,8,1,7,8,4,0,4,9,4,9,9,3,7,2,4,2,3,7,2,4,9
%N A196754 Decimal expansion of the least x>0 satisfying 1=3x*sin(x).
%H A196754 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196754 0.594839172505492954834899775377921510856777...
%t A196754 Plot[{1/x, Sin[x], 2 Sin[x], 3*Sin[x], 4 Sin[x]}, {x, 0, 2 Pi}]
%t A196754 t = x /. FindRoot[1/x == Sin[x], {x, .2, 1.4}, WorkingPrecision -> 100]
%t A196754 RealDigits[t]  (* A133866 *)
%t A196754 t = x /. FindRoot[1/x == 2 Sin[x], {x, .2, 1.4}, WorkingPrecision -> 100]
%t A196754 RealDigits[t]  (* A196624 *)
%t A196754 t = x /. FindRoot[1/x == 3 Sin[x], {x, .2, 1.4}, WorkingPrecision -> 100]
%t A196754 RealDigits[t]  (* A196754 *)
%t A196754 t = x /. FindRoot[1/x == 4 Sin[x], {x, .2, 1.4}, WorkingPrecision -> 100]
%t A196754 RealDigits[t]  (* A196755 *)
%t A196754 t = x /. FindRoot[1/x == 5 Sin[x], {x, .2, 1.4}, WorkingPrecision -> 100]
%t A196754 RealDigits[t]  (* A196756 *)
%t A196754 t = x /. FindRoot[1/x == 6 Sin[x], {x, .2, 1.4}, WorkingPrecision -> 100]
%t A196754 RealDigits[t]  (* A196757 *)
%Y A196754 Cf. A196758.
%K A196754 nonn,cons
%O A196754 0,1
%A A196754 _Clark Kimberling_, Oct 06 2011