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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
OFFSET
1,1
LINKS
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
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved