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Decimal expansion of (1/phi)^(1/phi), where phi is the golden ratio (1 + sqrt(5))/2 (A001622).
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%I #22 May 21 2020 18:58:21

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

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

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

%N Decimal expansion of (1/phi)^(1/phi), where phi is the golden ratio (1 + sqrt(5))/2 (A001622).

%C 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.

%H Alois P. Heinz, <a href="/A335020/b335020.txt">Table of n, a(n) for n = 0..10000</a>

%H Dr Peyam, <a href="https://www.youtube.com/watch?v=0IlWyIaMXqI">Derivative equals inverse</a>, youtube video (2018)

%F Equals (phi-1)^(phi-1), with phi = (1 + sqrt(5))/2.

%F Equals A094214^A094214.

%e 0.7427429446246816413695660476057885141497552527...

%p g:= (phi-> (1/phi)^(1/phi))((1+sqrt(5))/2):

%p evalf(g, 140);

%t RealDigits[(1/GoldenRatio)^(1/GoldenRatio), 10, 100][[1]] (* _Amiram Eldar_, May 21 2020 *)

%o (PARI) my(x=(sqrt(5)-1)/2); x^x \\ _Michel Marcus_, May 21 2020

%Y Cf. A001622, A094214, A185261.

%K nonn,cons

%O 0,1

%A _Alois P. Heinz_, May 19 2020