A092134 Continued fraction expansion for phi^phi, where phi is the golden ratio (1+sqrt(5))/2.

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, 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, 1, 2, 3, 3, 1, 2, 3, 1, 56, 1, 24, 6, 20, 3, 27, 2

Offset: 0

Author

Ryan Witko (witko(AT)nyu.edu), Mar 30 2004

Keywords

• nonn
• cofr
• changed

Examples

			2.178457.. = 2 + 1/(5 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...))))).
		

Crossrefs

Cf. A144749 (decimal expansion).

Programs

Maple

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

Mathematica

phi := (1 + Sqrt[5])/2; ContinuedFraction[phi^phi, 80] (* Bruno Berselli, Aug 07 2013 *)

PARI

gr = (1+sqrt(5))/2; contfrac(gr^gr) \\ Michel Marcus, Aug 07 2013

Extensions

a(12) and following terms corrected by Charles R Greathouse IV, Aug 07 2013

Offset changed by Andrew Howroyd, Aug 07 2024