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A201574 Decimal expansion of least x satisfying x^2 + 7 = csc(x) and 0 < x < Pi.

%I A201574 #13 Feb 07 2025 16:44:07
%S A201574 1,4,2,9,2,7,5,8,2,9,9,3,9,2,0,8,6,7,0,0,4,3,1,0,4,4,3,0,7,5,5,4,7,4,
%T A201574 8,2,4,0,8,8,4,3,5,1,3,9,9,1,0,5,0,9,4,5,4,0,2,7,8,5,0,1,0,4,5,9,2,8,
%U A201574 5,0,3,0,7,9,5,5,0,5,9,4,2,2,7,2,6,3,9,7,7,6,0,5,3,6,5,1,6,0,8
%N A201574 Decimal expansion of least x satisfying x^2 + 7 = csc(x) and 0 < x < Pi.
%C A201574 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201574 G. C. Greubel, <a href="/A201574/b201574.txt">Table of n, a(n) for n = 0..10000</a>
%H A201574 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201574 least:  0.14292758299392086700431044307554748240884...
%e A201574 greatest:  3.08092023229520680455935849821275370108...
%t A201574 a = 1; c = 7;
%t A201574 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201574 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201574 r = x /. FindRoot[f[x] == g[x], {x, .1, .2}, WorkingPrecision -> 110]
%t A201574 RealDigits[r]   (* A201574 *)
%t A201574 r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
%t A201574 RealDigits[r]   (* A201575 *)
%o A201574 (PARI) a=1; c=7; solve(x=0.1, .2, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018
%Y A201574 Cf. A201564.
%K A201574 nonn,cons
%O A201574 0,2
%A A201574 _Clark Kimberling_, Dec 03 2011