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
KEYWORD
nonn,cons
AUTHOR
Jonathan Sondow, Aug 28 2011
STATUS
approved