A364931 Decimal expansion of the solution to 1 / (1 + e^(-x)) = x.

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

Offset

0,1

Comments

Fixed point of sigmoid (standard logistic function) as well as its inverse (logit).

Links

Table of n, a(n) for n=0..99.

Eric Weisstein's World of Mathematics, Sigmoid Function.

Wikipedia, Logistic Function.

Example

0.6590460684074066...

Maple

Digits:=100: fsolve(1/(1+exp(-x))-x, x);

Mathematica

RealDigits[FindRoot[1/(1+Exp[-x])-x, {x, 0.6}, WorkingPrecision -> 100][[1, 2]], 10, 100][[1]]

Prog

(PARI) default(realprecision, 100); solve(x=0.4, 0.7, 1/(1+exp(-x))-x)

Crossrefs

Sequence in context: A272696 A048236 A193719 * A195700 A275110 A011284

Adjacent sequences: A364928 A364929 A364930 * A364932 A364933 A364934

Keyword

nonn,cons

Author

Michal Paulovic, Aug 13 2023

Status

approved