A092134 -id:A092134 - cp's OEIS frontend

A181779 Duplicate of A092134.

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

Michel Lagneau

dead

Previous name was: Continued fraction for phi^phi.

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

H. Walser, The Golden Section, Math. Assoc. of Amer, Washington DC 2001.
C. J. Willard, Le nombre d'or, Magnard, Paris 1987.

Cf. A144749 (decimal expansion).

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

ContinuedFraction[GoldenRatio^ GoldenRatio, 100 ]

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

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

A144749 Decimal expansion of the golden ratio powered to itself.

Original entry on oeis.org

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

Offset: 1

R. J. Mathar, Sep 20 2008

See A092134 for the continued fraction of this value, phi^phi, where phi = (sqrt(5)+1)/2 = A001622. - M. F. Hasler, Oct 08 2014

			Equals 2.178457567937599147372545702871245851807043301693254611347781924...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for transcendental numbers.

Cf. A001622, A104457, A098317, A094214, A139339, A139340, A144713.

RealDigits[N[GoldenRatio^GoldenRatio,200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)

(t=(sqrt(5)+1)/2)^t \\ Use \p99 to get 99 digits; digits(%\.1^99) for the sequence of digits. - M. F. Hasler, Oct 08 2014

numerical_approx(golden_ratio^golden_ratio, digits=120) # G. C. Greubel, Jun 16 2022

Equals A001622^A001622.

cp's OEIS Frontend

A181779 Duplicate of A092134.

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