login
A073822
Decimal expansion of number with continued fraction expansion 0, 1, 1, 2, 3, 5, ... (the Fibonacci numbers).
4
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
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
KEYWORD
cons,nonn
AUTHOR
Rick L. Shepherd, Aug 12 2002
STATUS
approved