cp's OEIS Frontend

A216863 The decimal expansion of the maximal zero x(3) of the function F(x) = f(f(x)) - x, where f(x) = cos(x) - sin(x).

%I A216863 #40 Jan 15 2014 04:46:00
%S A216863 1,4,1,2,7,9,4,5,8,5,7,2,7,6,2,2,2,4,5,2,9,3,5,7,7,5,8,6,5,0,6,6,3,7,
%T A216863 6,3,2,1,2,4,5,5,8,8,9,1,2,7,3,8,1,5,1,6,5,8,6,4,1,7,7,5,2,5,5,3,0,1,
%U A216863 1,2,5,2,4,7,7,1,2,2,0,5,5,1,8,2,4,3,3,4,0,8,7,8,5,0,0,6,0,8,9,2,5,6,1,5,0
%N A216863 The decimal expansion of the maximal zero x(3) of the function F(x) = f(f(x)) - x, where f(x) = cos(x) - sin(x).
%C A216863 The decimal expansions of the only other zeros x(1) and x(2) of F(x) are given in A216891 and A206291. See the comments in A216891 for more information about intriguing properties of these zeros.
%H A216863 R. Witula, D. Slota and Szeged Problem Group "Fejentalaltuka", <a href="http://www.jstor.org/stable/40391181">An Iteration Convergence: 11318[2007, 745]</a>, Amer. Math. Monthly, 116 No 7 (2009), 648-649.
%e A216863 We have x(3) = 1.4127945857276222... < sqrt(2).
%t A216863 f[x_] := Cos[x] - Sin[x];
%t A216863 FindRoot[f[f[x]] - x, {x, 1.4}, WorkingPrecision -> 110] (* _T. D. Noe_, Sep 24 2012; first line by _Rick L. Shepherd_, Jan 04 2014 *)
%o A216863 (PARI)
%o A216863 default(realprecision,110);
%o A216863 f(x) = cos(x) - sin(x);
%o A216863 solve(x = 1.4, 1.5, f(f(x)) - x) \\ _Rick L. Shepherd_, Jan 03 2014
%Y A216863 Cf. A216891, A206291, A215668, A215670, A215832, A215833, A168546.
%K A216863 nonn,cons
%O A216863 1,2
%A A216863 _Roman Witula_, Sep 18 2012
%E A216863 Offset corrected by _Rick L. Shepherd_, Jan 03 2014