A329458 - OEIS

%I #54 Jul 14 2020 09:11:09

%S 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,

%T 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,

%U 7,0,7,9,9,6,1,1,9,9,0,2,9

%N Decimal expansion of x such that x^x * log(x) - x^x + 1 = 0, x > 1.

%C Equivalent to the coordinates of the self-intersection point of the graph y^x - x^y = y - x, where x, y > 1.

%F x^x * log(x) - x^x + 1 = 0; x != 1.

%F y^x - x^y = y - x; y = x; x != 1.

%F x = exp(1-x^(-x)); x > 1. - _Rick Novile_, Jul 14 2020

%e x = 2.41173993056055928114518919802446413261177356034046370153515467138607...

%t FindRoot[x^x Log[x] - x^x + 1 == 0, {x, 2.40737, 2.41474}, WorkingPrecision -> 1000]

%o (PARI) solve(x=2, 3, x^x * log(x) - x^x + 1) \\ _Michel Marcus_, Nov 16 2019

%o (PARI) solve(x=2, 3, x - exp(1-1/x^x)) \\ _Michel Marcus_, Jul 14 2020

%Y Cf. A073226 (e^e), A194622, A194623, A194556, A194557.

%K nonn,cons

%O 1,1

%A _Rick Novile_, Nov 16 2019