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A201522 Decimal expansion of greatest x satisfying 6*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201522 #11 Jan 30 2025 15:41:52
%S A201522 1,4,8,9,4,8,0,6,5,6,7,3,1,8,3,3,3,2,0,3,9,9,1,2,6,0,1,7,6,7,7,3,1,7,
%T A201522 5,4,4,9,4,3,3,6,9,1,4,8,0,6,1,5,0,7,0,4,7,3,0,5,6,8,8,5,1,9,2,7,5,0,
%U A201522 4,5,7,7,5,1,2,6,7,8,1,6,2,9,7,4,3,0,6,2,3,7,3,9,0,3,5,3,3,5,5
%N A201522 Decimal expansion of greatest x satisfying 6*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201522 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201522 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201522 least:  0.60805447799791305332799572251089761...
%e A201522 greatest: 1.489480656731833320399126017677317...
%t A201522 a = 6; c = -1;
%t A201522 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201522 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201522 r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t A201522 RealDigits[r]   (* A201521 *)
%t A201522 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201522 RealDigits[r]   (* A201522 *)
%Y A201522 Cf. A201397.
%K A201522 nonn,cons
%O A201522 1,2
%A A201522 _Clark Kimberling_, Dec 02 2011