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A201422 Decimal expansion of least x satisfying 10*x^2 = sec(x) and 0 < x < Pi.

%I A201422 #10 Jan 30 2025 15:40:35
%S A201422 3,2,4,8,3,5,7,6,2,5,5,2,6,7,2,6,3,4,3,2,7,2,1,6,8,9,0,5,9,1,8,3,5,7,
%T A201422 0,3,0,0,8,4,8,6,6,5,9,6,3,0,4,6,3,6,6,2,0,1,2,2,0,0,8,0,9,3,4,7,0,4,
%U A201422 7,3,0,6,0,5,4,5,6,0,1,9,8,7,1,0,1,7,2,5,7,1,5,1,3,9,3,5,8,7,8
%N A201422 Decimal expansion of least x satisfying 10*x^2 = sec(x) and 0 < x < Pi.
%C A201422 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201422 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201422 least:  0.3248357625526726343272168905918357...
%e A201422 greatest: 1.52794989469861441964924475246801...
%t A201422 a = 10; c = 0;
%t A201422 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201422 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201422 r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
%t A201422 RealDigits[r]    (* A201422 *)
%t A201422 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201422 RealDigits[r]    (* A201423 *)
%Y A201422 Cf. A201397.
%K A201422 nonn,cons
%O A201422 0,1
%A A201422 _Clark Kimberling_, Dec 02 2011