Search: id:A091831
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%I A091831
%S A091831 1,3,8,33,35,39201,39203,60245508192801,60245508192803,
%T A091831 218662352649181293830957829984632156775201,
%U A091831 218662352649181293830957829984632156775203
%N A091831 Pierce expansion of 1/sqrt(2).
%C A091831 If u(0)=exp(1/m) m integer>1 and u(n+1)=u(n)/frac(u(n)) then floor(u(n))=m*n
%D A091831 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.
%H A091831 Author?, <a href="http://www.econ.upf.es/deehome/what/wpapers/postscripts/
               340.pdf">On a problem of Alfred Renyi </a>
%H A091831 Vlado Keselj, <a href="http://www.cs.uwaterloo.ca/cs-archive/CS-1996/
               21/cs-96-21.pdf">Length of Finite Pierce Series: Theoretical Analysis 
               and Numerical Computations </a>.
%H A091831 J. O. Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/Papers/sppe.ps">
               Some predictable Pierce expansions</a>, Fib. Quart., 22 (1984), 332-335.
%H A091831 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PierceExpansion.html">Pierce Expansion</a>
%F A091831 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))
%F A091831 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)...
%F A091831 limit n -> infty a(n)^(1/n)=e
%o A091831 (PARI) r=sqrt(2);for(n=1,10,r=r/(r-floor(r));print1(floor(r),","))
%Y A091831 Cf. A006275, A006276, A006283.
%Y A091831 Cf. A006784 (Pierce expansion definition), A028254
%Y A091831 Sequence in context: A094610 A064316 A009438 this_sequence A148916 A148917 
               A120892
%Y A091831 Adjacent sequences: A091828 A091829 A091830 this_sequence A091832 A091833 
               A091834
%K A091831 nonn
%O A091831 0,2
%A A091831 Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 09 2004

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