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Search: id:A091846
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| A091846 |
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Pierce expansion of log(2). |
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+0
1
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| 1, 3, 12, 21, 51, 57, 73, 85, 96, 1388, 4117, 5268, 9842, 11850, 16192, 19667, 29713, 76283, 460550, 1333597, 1462506, 9400189, 13097390, 30254851, 190193800, 201892756, 431766247, 942050077, 6204785761, 16684400052, 23762490104
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If u(0)=exp(1/m) m integer>=1 and u(n+1)=u(n)/frac(u(n)) then floor(u(n))=m*n
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REFERENCES
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P. Erdos and J. O. Shallit, New bounds on the length of finite Pierce and Engel series, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no.1, 43-53.
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LINKS
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Author?, On a problem of Alfred Renyi
Vlado Keselj, Length of Finite Pierce Series: Theoretical Analysis and Numerical Computations .
J. O. Shallit, Some predictable Pierce expansions, Fib. Quart., 22 (1984), 332-335.
Eric Weisstein's World of Mathematics, Pierce Expansion
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FORMULA
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Let u(0)=1/log(2) and u(n+1)=u(n)/frac(u(n)) where frac(x) is the fractional part of x, then a(n)=floor(u(n))
log(2) = 1/a(1) - 1/a(1)/a(2) + 1/a(1)/a(2)/a(3) - 1/a(1)/a(2)/a(3)/a(4)...
limit n--> infty a(n)^(1/n)=e
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PROGRAM
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(PARI) r=1/log(2); for(n=1, 30, r=r/(r-floor(r)); print1(floor(r), ", "))
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CROSSREFS
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Cf. A006275, A006276, A006283, A006284.
Cf. A006784 (Pierce expansion definition), A059180.
Sequence in context: A052217 A119507 A044436 this_sequence A061262 A051656 A074004
Adjacent sequences: A091843 A091844 A091845 this_sequence A091847 A091848 A091849
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 09 2004
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