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Search: id:A058580
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| A058580 |
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a(n) is the least natural number m such that the fractional part of m*(2^0.5) is less than 2^(-n). |
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2
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| 1, 3, 5, 17, 29, 29, 99, 169, 577, 985, 985, 3363, 5741, 19601, 33461, 33461, 114243, 195025, 195025, 1136689, 1136689
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Since 2^0.5 is irrational such m must exist because for any irrational number a the sequence a,2a,3a,4a,5a,... is dense modulo 1.
All terms are contained in A079496. - R. Stephan, Sep 09 2004
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FORMULA
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a(n) = min m such that m*(2^0.5)-floor(m*(2^0.5)) < 2^(-n)
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EXAMPLE
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a(7) = 99 because 99*(2^0.5) = 140.00714267... and 0.00714267... < 2^(-7) = 0.0078125 and 99 is the least natural number that satisfies this inequality.
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PROGRAM
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(PARI) o=1:for(n=1, 50, for(m=o, 10^9, if(frac(sqrt(2)*m)<2^(-n), print1(m", "):o=m:break)))
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CROSSREFS
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Sequence in context: A025111 A032619 A030077 this_sequence A161682 A079373 A038703
Adjacent sequences: A058577 A058578 A058579 this_sequence A058581 A058582 A058583
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KEYWORD
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nonn
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AUTHOR
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Avi Peretz (njk(AT)netvision.net.il), Dec 25 2000
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EXTENSIONS
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More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 27 2003
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