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A073115
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Decimal expansion of S = sum( k>=0,1/2^floor(k*PHI) ) where PHI is the golden ratio (1+sqrt(5))/2.
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3
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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
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number whose digits are obtained from the substitution system (1->(1,0),0->(1)). The n-th term of the continued fraction expansion for S is 2^Fibonacci(n-2) ) (cf. A000301) . This number is known to be transcendental.
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REFERENCES
| S. Wolfram,"A new kind of science", p. 913
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MATHEMATICA
| Take[ RealDigits[ Sum[N[1/2^Floor[k*GoldenRatio], 120], {k, 0, 300}]][[1]], 105] (* From Jean-François Alcover, Jul 28 2011 *)
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CROSSREFS
| Equals 1+A014565.
Sequence in context: A093444 A021858 A014565 * A176444 A197025 A096408
Adjacent sequences: A073112 A073113 A073114 * A073116 A073117 A073118
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KEYWORD
| cons,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 19 2002
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