

A199550


Decimal expansion of the positive root of x^x^x = 2.


2



1, 4, 7, 6, 6, 8, 4, 3, 3, 7, 3, 5, 7, 8, 6, 9, 9, 4, 7, 0, 8, 9, 2, 3, 5, 5, 8, 5, 3, 7, 3, 8, 8, 9, 8, 3, 8, 6, 5, 5, 1, 6, 8, 9, 3, 0, 9, 8, 5, 5, 2, 6, 9, 8, 4, 4, 6, 4, 4, 0, 3, 1, 4, 7, 6, 2, 1, 6, 9, 8, 0, 0, 2, 9, 1, 8, 8, 2, 1, 5, 2, 8, 5, 9, 7, 1, 4, 7, 2, 4, 0, 8, 4, 4, 0, 2, 6, 9, 5, 7, 9, 8, 3, 2, 2
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OFFSET

1,2


COMMENTS

As follows from Gelfond's theorem, the root is irrational, so this sequence is infinite and aperiodic. Its transcendence is, apparently, still an open problem.  Vladimir Reshetnikov, Apr 27 2013


LINKS

Table of n, a(n) for n=1..105.
Ash J. Marshall and Yiren Tan, A rational number of the form a^a with a irrational, Mathematical Gazette 96, March 2012, pp. 106109.
Eric Weisstein's World of Mathematics, Gelfond's Theorem


EXAMPLE

1.4766843373578699470892355853738898386551689309855269844644...


MATHEMATICA

First[RealDigits[Root[{Function[x, x^x^x  2], 1.477`4}], 10, 100]]


PROG

(PARI) solve(x=1, 2, x^x^x2) \\ Charles R Greathouse IV, Apr 14 2014


CROSSREFS

Cf. A030798.
Sequence in context: A116081 A275162 A105228 * A292510 A284116 A200353
Adjacent sequences: A199547 A199548 A199549 * A199551 A199552 A199553


KEYWORD

nonn,cons,easy


AUTHOR

Vladimir Reshetnikov, Nov 07 2011


STATUS

approved



