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A073115 Decimal expansion of sum(k>=0, 1/2^floor(k*phi) ) where phi = (1+sqrt(5))/2. 3
1, 7, 0, 9, 8, 0, 3, 4, 4, 2, 8, 6, 1, 2, 9, 1, 3, 1, 4, 6, 4, 1, 7, 8, 7, 3, 9, 9, 4, 4, 4, 5, 7, 5, 5, 9, 7, 0, 1, 2, 5, 0, 2, 2, 0, 5, 7, 6, 7, 8, 6, 0, 5, 1, 6, 9, 5, 7, 0, 0, 2, 6, 4, 4, 6, 5, 1, 2, 8, 7, 1, 2, 8, 1, 4, 8, 4, 6, 5, 9, 6, 2, 4, 7, 8, 3, 1, 6, 1, 3, 2, 4, 5, 9, 9, 9, 3, 8, 8, 3, 9, 2, 6, 5, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number whose digits are obtained from the substitution system (1->(1,0),0->(1)).

The n-th term of the continued fraction is 2^Fibonacci(n-2) ) (cf. A000301).

This number is known to be transcendental.

REFERENCES

J. L. Davison, A series and its associated continued fraction, Proc. Amer. Math. Soc. 63 (1977), pp. 29-32.

S. Wolfram,"A new kind of science", p. 913

LINKS

Table of n, a(n) for n=1..105.

FORMULA

Equals 1 + A014565.

EXAMPLE

1.70980344286129131464178739944457559701250220576786...

MATHEMATICA

Take[ RealDigits[ Sum[N[1/2^Floor[k*GoldenRatio], 120], {k, 0, 300}]][[1]], 105] (* Jean-Fran├žois Alcover, Jul 28 2011 *)

PROG

(PARI) phi=(1+sqrt(5))/2; suminf(n=0, 2.^-(n*phi\1)) \\ Charles R Greathouse IV, Jul 22 2013

CROSSREFS

Sequence in context: A093444 A021858 A014565 * A176444 A197025 A096408

Adjacent sequences:  A073112 A073113 A073114 * A073116 A073117 A073118

KEYWORD

cons,nonn

AUTHOR

Benoit Cloitre, Aug 19 2002

STATUS

approved

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Last modified December 22 16:00 EST 2014. Contains 252364 sequences.