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A196769 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/4).

%I A196769 #9 Apr 10 2021 02:01:12
%S A196769 1,5,0,9,5,0,6,8,3,2,2,2,4,4,7,2,8,8,5,5,6,5,3,2,6,2,2,0,4,3,7,7,6,8,
%T A196769 5,0,5,5,3,2,8,8,0,8,1,7,0,6,6,7,1,9,6,4,6,6,6,7,2,3,7,1,0,6,1,3,4,3,
%U A196769 0,5,4,2,1,6,9,1,4,0,3,4,8,1,5,9,4,3,3,3,4,5,5,5,4,1,1,9,2,2,0,1
%N A196769 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/4).
%e A196769 x=1.5095068322244728855653262204377685055328808170667196...
%t A196769 Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,
%t A196769   0, 2 Pi}]
%t A196769 t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
%t A196769 RealDigits[t]  (* A133866 *)
%t A196769 t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]
%t A196769 RealDigits[t]     (* A196767 *)
%t A196769 t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]
%t A196769 RealDigits[t]   (* A196768 *)
%t A196769 t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]
%t A196769 RealDigits[t]    (* A196769 *)
%t A196769 t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]
%t A196769 RealDigits[t]   (* A196770 *)
%t A196769 t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]
%t A196769 RealDigits[t]    (* A196771 *)
%Y A196769 Cf. A196772.
%K A196769 nonn,cons
%O A196769 1,2
%A A196769 _Clark Kimberling_, Oct 06 2011