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Continued fraction for phi^phi.
0

%I #20 Jul 08 2024 10:39:34

%S 2,5,1,1,1,1,10,1,1,2,8,7643,4,1,51,2,2,8,5,2,1,6,5,4,1,42,2,1,1,1,1,

%T 1,1,1,6,2,6,2,12,2,1,6,3,13,11,2,9,2,1,4,1,2,1,6,3,1,1,1,11,3,1,2,1,

%U 1,2,3,3,1,2,3,1,56,1,24,6,20,3,27,2,1,2,1,2,5,2,1,1,14,1,91,1,2,1,1,5,1,1,1,1,1,1,1,36,1,1,1,4,1,1,2,1,1,1,1,1,2,1,1,16,21

%N Continued fraction for phi^phi.

%D H. Walser, The Golden Section, Math. Assoc. of Amer, Washington DC 2001.

%D C. J. Willard, Le nombre d'or, Magnard, Paris 1987.

%e 2.178457567937599147372545... = 2 + 1/(5 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...))))).

%p with(numtheory):Digits:= 300: x:=(sqrt(5)+1)/2:convert(evalf(x^x), confrac);

%t ContinuedFraction[GoldenRatio^ GoldenRatio, 100 ]

%o (PARI) phi=(1+sqrt(5))/2;contfrac(phi^phi) \\ _Charles R Greathouse IV_, Jul 29 2011

%Y Cf. A144749 (decimal expansion).

%K nonn,cofr

%O 0,1

%A _Michel Lagneau_

%E Offset changed and missing term inserted by _Andrew Howroyd_, Jul 08 2024