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A201526 Decimal expansion of greatest x satisfying 8*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201526 #10 Jan 30 2025 15:43:02
%S A201526 1,5,1,3,0,0,5,7,3,7,4,4,7,7,4,9,0,9,7,7,7,4,6,9,3,0,5,4,0,1,2,0,7,0,
%T A201526 4,4,6,0,1,9,5,5,8,8,8,6,9,4,3,2,2,3,4,2,0,4,7,3,9,1,8,7,6,1,2,1,5,8,
%U A201526 8,2,8,9,4,5,6,1,0,7,7,4,1,4,7,8,7,3,8,0,0,8,6,2,7,8,8,7,6,6,3
%N A201526 Decimal expansion of greatest x satisfying 8*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201526 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201526 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201526 least:  0.518577002201711458253109820417244...
%e A201526 greatest: 1.5130057374477490977746930540120...
%t A201526 a = 8; c = -1;
%t A201526 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201526 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201526 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A201526 RealDigits[r]   (* A201525 *)
%t A201526 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201526 RealDigits[r]   (* A201526 *)
%Y A201526 Cf. A201397.
%K A201526 nonn,cons
%O A201526 1,2
%A A201526 _Clark Kimberling_, Dec 02 2011