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A258500 Decimal expansion of the nontrivial real solution of x^(3/2) = (3/2)^x. 2
7, 4, 0, 8, 7, 6, 4, 6, 8, 6, 9, 6, 5, 7, 7, 4, 5, 2, 1, 9, 5, 7, 2, 9, 5, 0, 2, 8, 5, 1, 0, 6, 1, 4, 3, 8, 9, 8, 0, 4, 1, 7, 1, 1, 4, 1, 0, 7, 4, 0, 0, 0, 1, 5, 1, 8, 2, 2, 7, 1, 8, 3, 9, 3, 7, 9, 1, 7, 0, 7, 1, 7, 1, 0, 0, 1, 3, 8, 4, 0, 2, 2, 8, 4, 2, 1, 8, 2, 3, 1, 1, 9, 2, 3, 0, 4, 7, 0, 6, 6, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..101.

Jonathan Sondow, Diego Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164.

FORMULA

x0 = -((x*ProductLog(-1, -(log(x)/x)))/log(x)), with x = 3/2, where ProductLog is the Lambert W function.

EXAMPLE

x0 = 7.408764686965774521957295028510614389804171141074...

z = x0^(3/2) = 20.16595073003535058942970947434890012034363496 ...

z > e^e = 15.15426224... = A073226.

MATHEMATICA

x0 = -((x*ProductLog[-1, -(Log[x]/x)])/Log[x]) /. x -> 3/2; RealDigits[x0, 10, 101] // First

CROSSREFS

Cf. A073226, A194556, A194557, A258501 (x^(5/2)=(5/2)^x), A258502 (x^(7/2)=(7/2)^x).

Sequence in context: A199955 A196624 A157413 * A243308 A293609 A294514

Adjacent sequences:  A258497 A258498 A258499 * A258501 A258502 A258503

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Jun 01 2015

STATUS

approved

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Last modified April 13 10:24 EDT 2021. Contains 342935 sequences. (Running on oeis4.)