Search: id:A058842
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%I A058842
%S A058842 1,3,1,3,9,27,81,243,217,651,1953,1763,5289,15867,14833,44499,2425,
%T A058842 7275,21825,65475,196425,589275,1767825,5303475,15910425,47731275,
%U A058842 8976097,26928291,80784873,242354619,727063857,2181191571,6543574713
%N A058842 From Renyi's "beta expansion of 1 in base 3/2": sequence gives a(1), 
               a(2), ... where x(n) = a(n)/2^n, with 0 < a(n) < 2^n, a(1) = 1, a(n) 
               = 3*a(n-1) modulo 2^n.
%C A058842 Let r be a real number strictly between 1 and 2, x any real number between 
               0 and 1; define y = (y(i)) by x(0) = x; x(i+1) = r*x(i)-1 if r*x(i)>
               1 and r*x(i) otherwise; y(i) = integer part of x(i+1): y = (y(i)) 
               is an infinite word on the alphabet (0,1). Here we take r = 3/2 and 
               x = 1.
%C A058842 It seems that the sequence x(n) = a(n)/2^n which satisfies 0<x(n)<1 is 
               not equidistributed in (0,1) and perhaps lim n -> infinity sum(k=1,
               n,x(k))/n = C < 0.4 < 1/2 - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Aug 27 2002
%D A058842 A. Renyi (1957), Representation for real numbers and their ergodic properties, 
               Acta. Math. Acad. Sci. Hung., 8, 477-493.
%F A058842 Let x(1)=1 x(n+1)=(3/2)*x(n) -floor((3/2)*x(n)); then a(n)=x(n)*2^n - 
               Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 27 2002
%Y A058842 Cf. A058841, A058840.
%Y A058842 Sequence in context: A088442 A037095 A146436 this_sequence A155734 A128162 
               A067329
%Y A058842 Adjacent sequences: A058839 A058840 A058841 this_sequence A058843 A058844 
               A058845
%K A058842 nonn,nice,easy
%O A058842 1,2
%A A058842 Claude Lenormand (claude.lenormand(AT)free.fr), Jan 05 2001
%E A058842 More terms from Larry Reeves (larryr(AT)acm.org), Feb 22 2001

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