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Search: id:A084119
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| A084119 |
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Decimal expansion of the Fibonacci binary number, sum(k>0, 1/2^F(k)), where F(k)=A000045(k). |
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+0
7
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| 1, 4, 1, 0, 2, 7, 8, 7, 9, 7, 2, 0, 7, 8, 6, 5, 8, 9, 1, 7, 9, 4, 0, 4, 3, 0, 2, 4, 4, 7, 1, 0, 6, 3, 1, 4, 4, 4, 8, 3, 4, 2, 3, 9, 2, 4, 5, 9, 5, 2, 7, 8, 7, 7, 2, 5, 9, 3, 2, 9, 2, 4, 6, 7, 9, 3, 0, 0, 7, 3, 5, 1, 6, 8, 2, 6, 0, 2, 7, 9, 4, 5, 3, 5, 1, 6, 1, 2, 3, 3
(list; cons; graph; listen)
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OFFSET
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1,2
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COMMENT
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The Fibonacci binary number 1.41027879720... is known to be transcendental.
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REFERENCES
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J. H. Loxton and A. van der Poorten, Bull. AMS 16 (1977), 15-47.
J. Shallit and A. van der Poorten, Can. J. Math. 45 (1993), 1067-79.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,20000
D. Bailey et al., On the binary expansions of algebraic numbers
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PROGRAM
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(PARI) suminf(k=1, 1/2^fibonacci(k))
(PARI) { default(realprecision, 20080); x=suminf(k=1, 1/2^fibonacci(k)); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b084119.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 04 2009]
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CROSSREFS
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Cf. A010056, A079586. See A124091 for another version.
Cf. A006518, A124091. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 04 2009]
Sequence in context: A124539 A096501 A062862 this_sequence A166073 A122899 A021713
Adjacent sequences: A084116 A084117 A084118 this_sequence A084120 A084121 A084122
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KEYWORD
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nonn,cons
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), May 18 2003
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EXTENSIONS
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Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009
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