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A073115
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Decimal expansion of sum(k>=0, 1/2^floor(k*phi) ) where phi = (1+sqrt(5))/2.
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6
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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
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1,2
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COMMENTS
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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.
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REFERENCES
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S. Wolfram, "A new kind of science", p. 913
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LINKS
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FORMULA
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EXAMPLE
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1.70980344286129131464178739944457559701250220576786...
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MATHEMATICA
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Take[ RealDigits[ Sum[N[1/2^Floor[k*GoldenRatio], 120], {k, 0, 300}]][[1]], 105] (* Jean-François Alcover, Jul 28 2011 *)
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PROG
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(PARI) phi=(1+sqrt(5))/2; suminf(n=1, (phi*n\1)/2^n) - 1 /* Michael Somos, May 22 2021 */
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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