A185067 Continued fraction for phi^gamma.

1, 3, 8, 9, 8, 1, 4, 2, 13, 4, 1, 2, 177, 3, 2, 1, 4, 18, 1, 7, 1, 3, 2, 2, 1, 4, 1, 5, 2, 6, 5, 5, 1, 1, 2, 2, 3, 1, 3, 7, 1, 2, 2, 1, 7, 126, 5, 3, 1, 1, 2, 1, 1, 2, 4, 1, 5, 3, 17, 4, 2, 4, 1, 2, 16, 7, 1, 9, 1, 4, 1, 26, 1, 2, 3, 3, 2, 1, 6, 14, 11, 1, 10, 1, 1, 3, 4, 4, 2, 1, 11

Offset

0,2

Comments

Gamma is Euler's constant (or the Euler-Mascheroni constant) and phi is the golden ratio.

Links

G. C. Greubel, Table of n, a(n) for n = 0..4999

Example

phi^gamma = 1.320173283762780841279163178... = 1 + 1/(3 + 1/(8 + 1/(9 + 1/(8 + 1/(1 + ...))))).

Mathematica

ContinuedFraction[GoldenRatio^EulerGamma, 100 ]

Prog

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

Crossrefs

Cf. A001622, A345066 (decimal expansion).

Sequence in context: A388511 A079591 A179047 * A397027 A256955 A197040

Adjacent sequences: A185064 A185065 A185066 * A185068 A185069 A185070

Keyword

nonn,cofr

Author

Michel Lagneau, Feb 18 2011

Extensions

Offset set to 0 by Andrew Howroyd, Nov 25 2025

Status

approved