A394586 - OEIS

%I #9 Apr 19 2026 05:45:13

%S 3,3,1,2,4,6,9,1,6,7,5,3,0,3,9,5,7,2,3,2,4,3,8,5,1,4,2,5,1,1,0,1,5,8,

%T 9,7,7,6,0,1,3,7,0,6,2,3,8,1,4,2,8,2,5,0,7,8,4,0,8,8,1,3,4,9,8,3,3,4,

%U 6,0,7,3,2,1,2,2,4,7,1,6,0,0,0,8,6,8,0,5,1,5,9

%N Decimal expansion of the shape parameter that leads to the same mean and mode of the Weibull distribution.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Weibull_distribution">Weibull distribution</a>

%e 3.3124691675303957232438514251101589776...

%t RealDigits[x /. FindRoot[Gamma[1 + 1/x] == ((x-1)/x)^(1/x), {x, 3}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, Apr 19 2026 *)

%o (PARI) solve (x=3, 4, gamma(1+1/x) - ((x-1)/x)^(1/x))

%Y A394587 is the corresponding function value of mean and mode.

%Y Cf. A244009, A394584, A394585, A394588.

%K nonn,cons

%O 1,1

%A _Hugo Pfoertner_, Mar 25 2026