

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
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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 functionsee 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) 151164; 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



