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Search: id:A091833
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| A091833 |
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Pierce expansion of 1/zeta(2). |
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+0
1
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| 2, 4, 7, 22, 29, 51, 173, 210, 262, 417, 746, 12341, 207220, 498538, 1286415, 2351289, 3702952, 7664494, 54693034, 75971438, 269954954, 6674693008, 13449203581, 59799655308, 98912303039, 948887634688, 3557757020909, 5898230078743
(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)=Pi^2/6 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/zeta(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=zeta(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.
Cf. A006784 (Pierce expansion definition), A059186.
Sequence in context: A101805 A102984 A103017 this_sequence A026080 A071795 A059501
Adjacent sequences: A091830 A091831 A091832 this_sequence A091834 A091835 A091836
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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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