A199550 Decimal expansion of the positive root of x^x^x = 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

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. 106-109.

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^x-2) \\ Charles R Greathouse IV, Apr 14 2014

Crossrefs

Cf. A030798.

Sequence in context: A361351 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