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Search: id:A091831
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| A091831 |
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Pierce expansion of 1/sqrt(2). |
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+0
1
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| 1, 3, 8, 33, 35, 39201, 39203, 60245508192801, 60245508192803, 218662352649181293830957829984632156775201, 218662352649181293830957829984632156775203
(list; graph; listen)
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OFFSET
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0,2
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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)=sqrt(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))
1/sqrt(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=sqrt(2); for(n=1, 10, r=r/(r-floor(r)); print1(floor(r), ", "))
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CROSSREFS
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Cf. A006275, A006276, A006283.
Cf. A006784 (Pierce expansion definition), A028254
Adjacent sequences: A091828 A091829 A091830 this_sequence A091832 A091833 A091834
Sequence in context: A094610 A064316 A009438 this_sequence A120892 A109655 A001120
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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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