login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A258501 Decimal expansion of the nontrivial real solution of x^(5/2) = (5/2)^x. 2
2, 9, 7, 0, 2, 8, 7, 0, 5, 0, 2, 5, 5, 7, 5, 8, 7, 7, 9, 3, 7, 9, 9, 8, 4, 2, 9, 1, 0, 3, 1, 6, 8, 6, 3, 7, 3, 2, 3, 9, 5, 0, 4, 3, 9, 6, 3, 2, 7, 1, 5, 0, 2, 5, 4, 5, 3, 4, 5, 9, 0, 1, 4, 7, 2, 9, 3, 6, 1, 2, 1, 9, 6, 3, 5, 1, 0, 9, 9, 8, 5, 2, 8, 9, 3, 2, 8, 9, 1, 5, 5, 0, 9, 2, 8, 0, 9, 1, 4, 1, 3, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..102.

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 = 5/2, where ProductLog is the Lambert W function.

EXAMPLE

x0 = 2.97028705025575877937998429103168637323950439632715025453459...

z = x0^(5/2) = 15.20533715980107653442006557792026842686895921352582...

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

MATHEMATICA

x0 = -((x*ProductLog[-1, -(Log[x]/x)])/Log[x]) /. x -> 5/2; RealDigits[x0, 10, 102] // First

CROSSREFS

Cf. A073226, A194556, A194557, A258500 (x^(3/2)=(3/2)^x), A258502 (x^(7/2)=(7/2)^x).

Sequence in context: A324555 A318969 A021775 * A198842 A016596 A201616

Adjacent sequences:  A258498 A258499 A258500 * A258502 A258503 A258504

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Jun 01 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 12 17:48 EDT 2021. Contains 342929 sequences. (Running on oeis4.)