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A091831
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Pierce expansion of 1/sqrt(2).
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1
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1, 3, 8, 33, 35, 39201, 39203, 60245508192801, 60245508192803, 218662352649181293830957829984632156775201, 218662352649181293830957829984632156775203
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| 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
| 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
| 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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PROG
| (PARI) r=sqrt(2); for(n=1, 10, r=r/(r-floor(r)); print1(floor(r), ", "))
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CROSSREFS
| Cf. A006275, A006276, A006283.
Cf. A006784 (Pierce expansion definition), A028254
Sequence in context: A094610 A064316 A009438 * A148916 A148917 A120892
Adjacent sequences: A091828 A091829 A091830 * A091832 A091833 A091834
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 09 2004
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