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Search: id:A072113
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| A072113 |
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Continued fraction expansion of Hall and Tenenbaum constant. |
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+0
2
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| 0, 3, 23, 1, 1, 16, 1, 2, 1, 8, 1, 274, 3, 1, 5, 1, 2, 1, 16, 1, 3, 3, 2, 1, 4, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 16, 3, 3, 2, 1, 1, 1, 2, 69, 121, 1, 5, 1, 2, 1, 2, 1, 1, 1, 2, 1, 12, 4, 1, 1, 1, 1, 2, 1, 2, 3, 3, 1, 3, 2, 4, 1, 7, 1, 16, 2, 4, 1, 2, 7, 2, 3, 1, 3, 2, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 3, 2, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For any multiplicative function g with values -1<= g(k) <= 1, for any real x >=2, Sum( i<= x, g(i) ) << x * exp{ -K * Sum( p<=x, (1-g(p))/p ) } and K is the optimal constant satisfying this inequality ( Hall and Tenenbaum, 1991)
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REFERENCES
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G. Tenenbaum, Introduction \`a la th\'eorie analytique et probabiliste des nombres, p. 348, Publications de l'Institut Cartan, 1990.
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FORMULA
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K = cos(S) = 0.3287... where S it the root 0< S < 2Pi of sin(S)+(Pi-S)*cos(S) = Pi/2
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PROGRAM
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(PARI) \p200 contfrac(cos(solve(X=0, 2*Pi, sin(X)+(Pi-X)*cos(X)-Pi/2)))
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CROSSREFS
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Cf. A072112.
Adjacent sequences: A072110 A072111 A072112 this_sequence A072114 A072115 A072116
Sequence in context: A099750 A119770 A132558 this_sequence A105433 A088605 A063562
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KEYWORD
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base,cofr,easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 19 2002
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