Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Apr 09 2021 15:50:52
%S 1,4,0,0,1,0,2,5,5,5,3,3,6,9,4,1,7,4,1,8,3,1,9,5,9,3,7,1,5,7,1,5,8,5,
%T 4,7,3,0,5,3,8,8,4,6,9,6,6,3,4,1,9,0,6,0,7,3,0,4,4,3,6,4,3,4,4,5,2,6,
%U 9,3,7,2,9,0,5,1,9,5,1,5,7,0,3,3,9,8,8,1,7,5,6,5,2,3,4,9,1,0,1
%N Decimal expansion of the greater of two values of x satisfying 5*x^2 - 4 = tan(x) and 0 < x < Pi/2.
%C See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%e lesser: 1.0862483073723514930516537470257901302111...
%e greater: 1.4001025553369417418319593715715854730538...
%t a = 5; c = 4;
%t f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, .9, 1.0}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200626 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200627 *)
%Y Cf. A200614.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 20 2011