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 A194346 Decimal expansion of h_o(1/17), where h_o(x) is the odd infinite power tower function. 3
 2, 0, 4, 2, 7, 4, 7, 3, 6, 6, 6, 5, 5, 1, 8, 4, 9, 9, 1, 7, 5, 6, 9, 8, 7, 4, 5, 1, 8, 6, 4, 4, 6, 9, 5, 7, 9, 9, 1, 6, 6, 8, 6, 9, 0, 3, 4, 8, 4, 2, 2, 5, 7, 2, 7, 3, 6, 5, 9, 2, 4, 6, 6, 7, 5, 9, 3, 2, 4, 9, 6, 6, 1, 3, 3, 3, 3, 6, 6, 8, 4, 1, 4, 3, 5, 8, 7, 7, 1, 6, 3, 7, 2, 0, 1, 9, 7, 4, 6, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The odd infinite power tower function is h_o(x) = lim f(n,x) as n --> infinity, where f(n+1,x) = x^x^(f(n,x)) and f(1,x) = x. The even infinite power tower function h_e(x) is the same limit except with f(1,x) = x^x (see A194347). The limits exist if and only if 0 < x <= e^(1/e). If (1/e)^e <= x <= e^(1/e), then h_o(x) = h_e(x) = h(x) (the infinite power tower function-see the comments in A073230) and y = h(x) is a solution of x^y = y. If 0 < x < (1/e)^e, then h_o(x) < h_e(x), and two solutions of x^x^y = y are y = h_o(x) and y = h_e(x). For example, y = h_o(1/16) = 1/4 and y = h_e(1/16) = 1/2 are solutions of (1/16)^(1/16)^y = y. h_o(1/17) and h_e(1/17) are irrational, and at least one of them is transcendental (see Sondow and Marques 2010). REFERENCES See the References in Sondow and Marques 2010. LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164; see Definition 4.3, Figure 7, and top of p. 163. EXAMPLE 0.204274736665518499175698745186446957991668690348422572736592466759324966133336... MATHEMATICA a = N[1/17, 100]; Do[a = (1/17)^(1/17)^a, {3000}]; RealDigits[a, 10, 100] // First RealDigits[ Fold[ N[#2^#1, 128] &, 1/17, Table[1/17, {5710}]], 10, 105][[1]] (* Robert G. Wilson v, Mar 20 2012 *) PROG (PARI) solve(x=0, 1, 17^(-17^-x)-x) \\ Charles R Greathouse IV, Mar 20, 2012 CROSSREFS Cf. A073229, A073230, A073243, A194347. Sequence in context: A216960 A285348 A163123 * A328598 A284010 A278082 Adjacent sequences:  A194343 A194344 A194345 * A194347 A194348 A194349 KEYWORD nonn,cons AUTHOR Jonathan Sondow, Aug 27 2011 STATUS approved

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Last modified August 6 18:25 EDT 2020. Contains 336256 sequences. (Running on oeis4.)