A194625 - OEIS

A194625

Decimal expansion of the larger solution to x^x = 3/4.

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

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OFFSET

0,1

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

0.636262939294531019987513755204233173117867057936262294886540645406389214402799...

MATHEMATICA

x = x /. FindRoot[x^x == 3/4, {x, 0.7}, WorkingPrecision -> 120]; RealDigits[x, 10, 100] // First

CROSSREFS

Cf. A030798 (x^x = 2), A072364 ((1/e)^(1/e)), A194624 (smaller solution to x^x = 3/4).

Sequence in context: A008567 A233700 A195436 * A165065 A069938 A043296

Adjacent sequences: A194622 A194623 A194624 * A194626 A194627 A194628

KEYWORD

nonn,cons

AUTHOR

Jonathan Sondow, Sep 02 2011

STATUS

approved