A181779 Continued fraction for phi^phi.

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, 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

Offset

0,1

References

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

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

Links

Table of n, a(n) for n=0..119.

Example

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

Maple

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

Mathematica

ContinuedFraction[GoldenRatio^ GoldenRatio, 100 ]

Prog

(PARI) phi=(1+sqrt(5))/2; contfrac(phi^phi) \\ Charles R Greathouse IV, Jul 29 2011

Crossrefs

Cf. A144749 (decimal expansion).

Sequence in context: A124779 A284750 A092134 * A024548 A376316 A197737

Adjacent sequences: A181776 A181777 A181778 * A181780 A181781 A181782

Keyword

nonn,cofr

Author

Michel Lagneau

Extensions

Offset changed and missing term inserted by Andrew Howroyd, Jul 08 2024

Status

approved