A329458 Decimal expansion of x such that x^x * log(x) - x^x + 1 = 0, x > 1.
2, 4, 1, 1, 7, 3, 9, 9, 3, 0, 5, 6, 0, 5, 5, 9, 2, 8, 1, 1, 4, 5, 1, 8, 9, 1, 9, 8, 0, 2, 4, 4, 6, 4, 1, 3, 2, 6, 1, 1, 7, 7, 3, 5, 6, 0, 3, 4, 0, 4, 6, 3, 7, 0, 1, 5, 3, 5, 1, 5, 4, 6, 7, 1, 3, 8, 6, 0, 7, 0, 7, 9, 9, 6, 1, 1, 9, 9, 0, 2, 9
Offset: 1
Examples
x = 2.41173993056055928114518919802446413261177356034046370153515467138607...
Programs
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Mathematica
FindRoot[x^x Log[x] - x^x + 1 == 0, {x, 2.40737, 2.41474}, WorkingPrecision -> 1000] -
PARI
solve(x=2, 3, x^x * log(x) - x^x + 1) \\ Michel Marcus, Nov 16 2019
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PARI
solve(x=2, 3, x - exp(1-1/x^x)) \\ Michel Marcus, Jul 14 2020
Formula
x^x * log(x) - x^x + 1 = 0; x != 1.
y^x - x^y = y - x; y = x; x != 1.
x = exp(1-x^(-x)); x > 1. - Rick Novile, Jul 14 2020
Comments