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A194348
Decimal expansion of sqrt(2)^sqrt(2)^sqrt(2).
3
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
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.
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
KEYWORD
nonn,cons
AUTHOR
Jonathan Sondow, Aug 28 2011
STATUS
approved