

A225134


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


2



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

1,2


COMMENTS

It is unknown if this root is rational, algebraic irrational, or transcendental.


LINKS

Table of n, a(n) for n=1..105.
J. Marshall Ash and Yiren Tan, A rational number of the form a^a with a irrational, Mathematical Gazette 96, March 2012, pp. 106109.
Wikipedia, Tetration, Open questions


EXAMPLE

1.4466014324298641745973339875976614806873210422822800263639...


MATHEMATICA

RealDigits[FindRoot[x^x^x^x == 2, {x, 1}, WorkingPrecision > 110][[1, 2]], 10, 105][[1]]


PROG

(PARI) solve(x=1, 2, x^x^x^x2) \\ Charles R Greathouse IV, Apr 15 2014


CROSSREFS

Cf. A030798, A199550, A225153 (continued fraction), A225208 (Engel expansion).
Sequence in context: A078240 A296844 A016710 * A121064 A213342 A019559
Adjacent sequences: A225131 A225132 A225133 * A225135 A225136 A225137


KEYWORD

nonn,cons,easy


AUTHOR

Vladimir Reshetnikov, Apr 29 2013


STATUS

approved



