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A201417 Decimal expansion of greatest x satisfying 7*x^2 = sec(x) and 0 < x < Pi.

%I A201417 #10 Jan 30 2025 15:38:56
%S A201417 1,5,0,7,9,2,8,7,9,5,3,8,0,0,9,8,2,6,6,5,6,7,8,9,9,9,9,4,0,7,0,9,9,1,
%T A201417 4,1,3,3,9,9,6,3,0,1,1,4,6,2,2,2,1,0,4,1,8,0,3,0,5,4,5,7,3,5,2,6,3,9,
%U A201417 4,0,3,2,6,3,3,9,6,3,2,6,5,4,9,7,2,1,7,5,5,1,3,4,9,7,3,7,6,4,3
%N A201417 Decimal expansion of greatest x satisfying 7*x^2 = sec(x) and 0 < x < Pi.
%C A201417 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201417 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201417 least:  0.39327382732884150383245205720625342659...
%e A201417 greatest: 1.507928795380098266567899994070991413...
%t A201417 a = 7; c = 0;
%t A201417 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201417 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201417 r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
%t A201417 RealDigits[r]    (* A201416 *)
%t A201417 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201417 RealDigits[r]    (* A201417 *)
%Y A201417 Cf. A201397.
%K A201417 nonn,cons
%O A201417 1,2
%A A201417 _Clark Kimberling_, Dec 01 2011