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

Author

Rick L. Shepherd, Aug 12 2002

Keywords

• cons
• nonn

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

Examples

			0.58887395254893350767123112124...
		

Links

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

Crossrefs

Cf. A000045 (Fibonacci numbers).

Programs

Mathematica

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

PARI

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