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 A144738 Decimal expansion of constant related to a dynamical system involving the zeta function. 0
 5, 1, 2, 7, 3, 7, 9, 1, 5, 4, 5, 4, 9, 6, 9, 3, 3, 5, 3, 2, 9, 2, 2, 7, 0, 9, 9, 7, 0, 6, 0, 7, 5, 2, 9, 5, 1, 2, 4, 0, 4, 8, 2, 8, 4, 8, 4, 5, 6, 3, 7, 1, 9, 3, 6, 6, 1, 0, 0, 5, 0, 1, 3, 6, 2, 8, 3, 5, 5, 0, 4, 7, 7, 6, 5, 5, 9, 4, 4, 5, 7, 4, 1, 2, 2, 5, 9, 9, 1, 5, 9, 9, 8, 8, 8, 3, 0, 9, 6, 9, 0, 1, 6, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS If iterations of zeta function converge to the constant A069857 then the ratio of successive imaginary parts of the orbit converge to -c. I.e., let z(n+1) = zeta(z(n)) if lim_{n->oo} z(n) = A069857; then lim_{n->oo} imag(z(n+1))/imag(z(n)) = -0.512.... -c = zeta'(A069857). - Gerald McGarvey, Feb 22 2009 LINKS Table of n, a(n) for n=0..103. B. Brent, Experiments with zeta dynamics, Feb 2012. [Broken link] B. Brent, Experiments with the dynamics of the Riemann zeta function, arXiv:1703.08779 [math.NT], 2017. EXAMPLE c=0.51273791545496933532922709970607529512404828484563... MATHEMATICA digits = 104; A069857 = x /. FindRoot[ Zeta[x] == x, {x, 0}, WorkingPrecision -> digits+5]; Zeta'[A069857] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Mar 04 2013, after Gerald McGarvey *) PROG (PARI) -zeta'(solve(x=-1, 0, zeta(x)-x)) \\ Michel Marcus, May 05 2020 CROSSREFS Cf. A069857. Sequence in context: A195407 A011509 A361970 * A021199 A073324 A021665 Adjacent sequences: A144735 A144736 A144737 * A144739 A144740 A144741 KEYWORD cons,nonn AUTHOR Benoit Cloitre, Sep 20 2008 STATUS approved

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Last modified June 7 00:08 EDT 2023. Contains 363151 sequences. (Running on oeis4.)