OFFSET
0,1
COMMENTS
The real function f(x) = (1/phi)^(1/phi) x^phi satisfies the differential equation f'(x) = f^(-1)(x): the derivative of f equals the compositional inverse of f.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
Dr Peyam, Derivative equals inverse, youtube video (2018)
EXAMPLE
0.7427429446246816413695660476057885141497552527...
MAPLE
g:= (phi-> (1/phi)^(1/phi))((1+sqrt(5))/2):
evalf(g, 140);
MATHEMATICA
RealDigits[(1/GoldenRatio)^(1/GoldenRatio), 10, 100][[1]] (* Amiram Eldar, May 21 2020 *)
PROG
(PARI) my(x=(sqrt(5)-1)/2); x^x \\ Michel Marcus, May 21 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Alois P. Heinz, May 19 2020
STATUS
approved