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 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). 2
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Table of n, a(n) for n=1..105. R. Witula, D. Slota and Szeged Problem Group "Fejentalaltuka", An Iteration Convergence: 11318[2007, 745], Amer. Math. Monthly, 116 No 7 (2009), 648-649. EXAMPLE We have x(3) = 1.4127945857276222... < sqrt(2). MATHEMATICA f[x_] := Cos[x] - Sin[x]; 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 *) PROG (PARI) default(realprecision, 110); f(x) = cos(x) - sin(x); solve(x = 1.4, 1.5, f(f(x)) - x) \\ Rick L. Shepherd, Jan 03 2014 CROSSREFS Cf. A216891, A206291, A215668, A215670, A215832, A215833, A168546. Sequence in context: A241185 A243584 A084460 * A120578 A096249 A081454 Adjacent sequences: A216860 A216861 A216862 * A216864 A216865 A216866 KEYWORD nonn,cons AUTHOR Roman Witula, Sep 18 2012 EXTENSIONS Offset corrected by Rick L. Shepherd, Jan 03 2014 STATUS approved

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Last modified November 29 15:54 EST 2023. Contains 367445 sequences. (Running on oeis4.)