

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
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OFFSET

1,2


COMMENTS

Number whose digits are obtained from the substitution system (1>(1,0),0>(1)).
The nth term of the continued fraction is 2^Fibonacci(n2) ) (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. 2932.
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] (* JeanFrançois 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



