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A078333
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Decimal expansion of sqrt(2)^sqrt(2).
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8
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1, 6, 3, 2, 5, 2, 6, 9, 1, 9, 4, 3, 8, 1, 5, 2, 8, 4, 4, 7, 7, 3, 4, 9, 5, 3, 8, 1, 0, 2, 4, 7, 1, 9, 6, 0, 2, 0, 7, 9, 1, 0, 8, 8, 5, 7, 0, 5, 3, 1, 1, 4, 1, 1, 7, 2, 4, 7, 7, 8, 0, 6, 8, 4, 3, 8, 3, 0, 3, 5, 2, 0, 5, 9, 9, 8, 6, 1, 6, 6, 4, 2, 2, 4, 7, 8, 5, 5, 5, 0, 7, 5, 0, 6, 6, 2, 6, 0, 4, 1, 4, 2, 3, 0, 0
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OFFSET
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1,2
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COMMENTS
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This number was used in a non-constructive proof that an irrational number raised to an irrational power may be a rational number: "sqrt(2)^sqrt(2) is either rational or irrational. If it is rational, our statement is proved. If it is irrational, (sqrt(2)^sqrt(2))^sqrt(2) = 2 proves our statement." (Jarden, 1953). - Amiram Eldar, Aug 14 2020
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REFERENCES
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Paul R. Halmos, Problems for mathematicians, young and old, The Mathematical Association of America, 1991. Problem 3 B, pp. 22 and 171.
Dov Jarden, Curiosa No. 339: A simple proof that a power of an irrational number to an irrational exponent may be rational, Scripta Mathematica, Vol. 19 (1953), p. 229.
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LINKS
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J. P. Jones and S. Toporowski, Irrational numbers, American Mathematical Monthly, Vol. 80, No. 4 (1973), pp. 423-424.
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EXAMPLE
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sqrt(2)^sqrt(2) = 1.632526919438152844773495381...
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MATHEMATICA
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RealDigits[Sqrt[2]^Sqrt[2], 10, 111][[1]]
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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