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

Author

Vladimir Reshetnikov, Apr 29 2013

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			1.4466014324298641745973339875976614806873210422822800263639...
		

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.
• Wikipedia, Tetration, Open questions

Crossrefs

Cf. A030798, A199550, A225153 (continued fraction), A225208 (Engel expansion).

Programs

Mathematica

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

PARI

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