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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
OFFSET
1,2
COMMENTS
It is unknown if this root is rational, algebraic irrational, or transcendental.
LINKS
J. Marshall Ash and Yiren Tan, A rational number of the form a^a with a irrational, Mathematical Gazette 96, March 2012, pp. 106-109.
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^x-2) \\ Charles R Greathouse IV, Apr 15 2014
CROSSREFS
Cf. A030798, A199550, A225153 (continued fraction), A225208 (Engel expansion).
Sequence in context: A296844 A332917 A016710 * A121064 A213342 A019559
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved