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Search: id:A091832
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| A091832 |
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Pierce expansion of 1/e^2. |
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+0
1
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| 18, 19, 136, 349, 357, 1354, 6996, 7135, 9531, 11558, 15996, 17432, 52118, 151048, 427802, 821834, 877819, 972918, 1046690, 1540789, 3653077, 8200738, 9628573, 164153335, 5607624822, 86457467082, 141885251873, 151882622551
(list; graph; listen)
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OFFSET
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1,1
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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.
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FORMULA
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let u(0)=exp(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/e^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), A059194.
Sequence in context: A041670 A041672 A041674 this_sequence A041676 A041678 A056083
Adjacent sequences: A091829 A091830 A091831 this_sequence A091833 A091834 A091835
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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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