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

1,1

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

Equals A001622^A001622.

Example

Equals 2.178457567937599147372545702871245851807043301693254611347781924...

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A256392 A011134 A157240 * A021463 A371268 A371261

Adjacent sequences: A144746 A144747 A144748 * A144750 A144751 A144752

Keyword

cons,nonn

Author

R. J. Mathar, Sep 20 2008

Status

approved