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A201521 Decimal expansion of least x satisfying 6*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201521 #11 Jan 30 2025 15:41:42
%S A201521 6,0,8,0,5,4,4,7,7,9,9,7,9,1,3,0,5,3,3,2,7,9,9,5,7,2,2,5,1,0,8,9,7,6,
%T A201521 1,7,8,8,5,3,2,9,6,8,8,0,9,3,5,3,6,0,8,7,7,7,4,5,4,0,5,6,5,6,6,4,3,4,
%U A201521 7,5,2,1,6,4,7,2,0,8,0,8,5,1,2,1,0,0,0,3,6,7,9,4,8,7,2,9,3,4,4
%N A201521 Decimal expansion of least x satisfying 6*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201521 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201521 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201521 least:  0.60805447799791305332799572251089761...
%e A201521 greatest: 1.489480656731833320399126017677317...
%t A201521 a = 6; c = -1;
%t A201521 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201521 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201521 r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t A201521 RealDigits[r]   (* A201521 *)
%t A201521 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201521 RealDigits[r]   (* A201522 *)
%Y A201521 Cf. A201397.
%K A201521 nonn,cons
%O A201521 0,1
%A A201521 _Clark Kimberling_, Dec 02 2011