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A201525 Decimal expansion of least x satisfying 8*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201525 #12 Jan 30 2025 15:42:59
%S A201525 5,1,8,5,7,7,0,0,2,2,0,1,7,1,1,4,5,8,2,5,3,1,0,9,8,2,0,4,1,7,2,4,4,9,
%T A201525 9,4,8,3,1,0,4,3,3,3,7,0,3,4,8,6,2,9,7,2,7,1,9,3,3,8,9,8,0,8,1,5,4,5,
%U A201525 0,6,9,7,3,1,1,0,2,9,7,7,7,1,8,4,3,4,8,1,3,2,6,4,1,2,8,0,7,3,0
%N A201525 Decimal expansion of least x satisfying 8*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201525 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201525 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201525 least:  0.518577002201711458253109820417244...
%e A201525 greatest: 1.5130057374477490977746930540120...
%t A201525 a = 8; c = -1;
%t A201525 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201525 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201525 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A201525 RealDigits[r]   (* A201525 *)
%t A201525 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201525 RealDigits[r]   (* A201526 *)
%Y A201525 Cf. A201397.
%K A201525 nonn,cons
%O A201525 0,1
%A A201525 _Clark Kimberling_, Dec 02 2011