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A194624 Decimal expansion of the smaller solution to x^x = 3/4. 1
1, 5, 3, 5, 1, 6, 7, 8, 9, 6, 6, 3, 9, 5, 2, 9, 4, 7, 1, 5, 0, 0, 6, 8, 3, 3, 2, 9, 7, 8, 4, 6, 3, 2, 2, 7, 7, 1, 1, 2, 6, 9, 4, 8, 5, 4, 8, 9, 9, 6, 9, 6, 2, 0, 3, 1, 7, 9, 8, 5, 4, 2, 8, 3, 3, 4, 3, 7, 2, 6, 1, 3, 6, 4, 1, 9, 0, 5, 8, 3, 0, 2, 9, 3, 6, 8, 7, 6, 6, 0, 5, 3, 0, 1, 9, 3, 7, 1, 9, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Since (1/e)^(1/e) < 3/4 < 1, the equation x^x = 3/4 has two solutions x = a and x = b with 0 < a < 1/e < b < 1. Both solutions are transcendental (see Proposition 2.2 in Sondow-Marques 2010).
LINKS
Table of n, a(n) for n=0..99.
J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164.
Index entries for transcendental numbers
EXAMPLE
0.15351678966395294715006833297846322771126948548996962031798542833437261364190...
MATHEMATICA
x = x /. FindRoot[x^x == 3/4, {x, 0.1}, WorkingPrecision -> 120]; RealDigits[x, 10, 100] // First
CROSSREFS
Cf. A030798 (x^x = 2), A072364 ((1/e)^(1/e)), A194625 (larger solution to x^x = 3/4).
Sequence in context: A071050 A271780 A176036 * A239805 A333236 A270915
Adjacent sequences: A194621 A194622 A194623 * A194625 A194626 A194627
KEYWORD
nonn,cons
AUTHOR
Jonathan Sondow, Sep 02 2011
STATUS
approved

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Last modified August 18 23:05 EDT 2024. Contains 375284 sequences. (Running on oeis4.)