A073822 Decimal expansion of number with continued fraction expansion 0, 1, 1, 2, 3, 5, ... (the Fibonacci numbers).

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

Offset

0,1

Comments

Is anything known about the properties of this number? - Edray Herber Goins (ehgoins(AT)mac.com), Jun 27 2004

Wolf (2010), in addition to prime numbers, also ponders continued fractions from the factorials (f) and from the Fibonacci numbers (F), remarking that "both f and F also should be transcendental but we are not aware of the proof of this fact," and that the Davenport-Roth theorem is of no help. - Alonso del Arte, Mar 06 2012

Links

Table of n, a(n) for n=0..103.

Marek Wolf, "Continued fractions constructed from prime numbers" arXiv:1003.4015 [math.NT] Sep 26 2010

Example

0.58887395254893350767123112124...

Mathematica

RealDigits[FromContinuedFraction[Fibonacci[Range[0, 100]]], 10, 120][[1]] (* Harvey P. Dale, Mar 06 2012 *)

Prog

(PARI) dec_exp(v)= w=contfracpnqn(v); w[1, 1]/w[2, 1]+0. dec_exp(vector(1000, i, fibonacci(i-1)))

Crossrefs

Cf. A000045 (Fibonacci numbers).

Sequence in context: A265274 A365523 A200286 * A198606 A031165 A113729

Adjacent sequences: A073819 A073820 A073821 * A073823 A073824 A073825

Keyword

cons,nonn

Author

Rick L. Shepherd, Aug 12 2002

Status

approved