A144749 Decimal expansion of the golden ratio powered to itself.

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

Author

R. J. Mathar, Sep 20 2008

Keywords

• cons
• nonn

Comments

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

Examples

			Equals 2.178457567937599147372545702871245851807043301693254611347781924...
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

(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

SageMath

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

Formula

Equals A001622^A001622.