A194348 Decimal expansion of sqrt(2)^sqrt(2)^sqrt(2).

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

Offset

1,2

Comments

If Schanuel's Conjecture is true, then sqrt(2)^sqrt(2)^sqrt(2) is transcendental (see Marques and Sondow 2010, p. 79).

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

S. Finch, Errata and Addenda to Mathematical Constants, Jun 23 2012, Section 1.1

D. Marques and J. Sondow, Schanuel's conjecture and algebraic powers z^w and w^z with z and w transcendental, arXiv:1010.6216 [math.NT], 2010-2011; East-West J. Math., 12 (2010), 75-84.

Wikipedia, Schanuel's conjecture

Example

1.76083955588002809075664989563837274807980409431850990464638822505342...

Mathematica

RealDigits[ Sqrt[2]^Sqrt[2]^Sqrt[2], 10, 100] // First

Prog

(PARI) sqrt(2)^sqrt(2)^sqrt(2) \\ Charles R Greathouse IV, May 14 2014
(PARI) (x->x^x^x)(sqrt(2)) \\ Charles R Greathouse IV, May 14 2014
(Magma) SetDefaultRealField(RealField(100)); Sqrt(2)^Sqrt(2)^Sqrt(2); // G. C. Greubel, Aug 19 2018

Crossrefs

Cf. A002193 (decimal expansion of sqrt(2)), A078333 (decimal expansion of sqrt(2)^sqrt(2)), A194555 (the decimal expansion of the real part of I^e^Pi).

Sequence in context: A021572 A321079 A111764 * A094123 A132799 A154580

Adjacent sequences: A194345 A194346 A194347 * A194349 A194350 A194351

Keyword

nonn,cons

Author

Jonathan Sondow, Aug 28 2011

Status

approved