A225134 Decimal expansion of the positive root of x^x^x^x = 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

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. 106-109.

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^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

Adjacent sequences: A225131 A225132 A225133 * A225135 A225136 A225137

Keyword

nonn,cons,easy

Author

Vladimir Reshetnikov, Apr 29 2013

Status

approved