%I A093053
%S A093053 1,2,5,11,23,46,93,186,372,745,1490,2980,5960,11921,23843,47686,95373,
%T A093053 190746,381493,762986,1525973,3051946,6103893,12207787,24415575,
%U A093053 48831150,97662301,195324602,390649204,781298409,1562596819,3125193638
%N A093053 Continued fraction expansion of a constant x such that the n-th partial 
               quotient equals a(n) = floor(2^n*x), with a(0)=1.
%C A093053 Decimal expansion is given by A093054. The partial quotients of the continued 
               fraction expansion of 2^m*x include many similar terms. For example, 
               the continued fraction of 2*x is given by: [2;1,10,5,1,1,11,92,46,
               1,1,92,1,1,185,1,1,372,2980,1490,11920,5960,1,1,11921,95372,47686,
               1,1,95372,1,1,...].
%e A093053 x=[1;2,5,11,23,46,93,186,372,745,1490,2980,5960,11921,23843,...].
%e A093053 x=1.455281692832971051393034444524589699271213777825554774132070945742167...
%p A093053 {L=500;x=sqrt(2);for(i=1,10, cf=vector(L,n,floor(x*2^(n-1))); cm=contfracpnqn(cf);
               x=cm[1,1]/cm[2,1])}
%Y A093053 Cf. A093054.
%Y A093053 Sequence in context: A005986 A147878 A140992 this_sequence A075712 A000100 
               A083005
%Y A093053 Adjacent sequences: A093050 A093051 A093052 this_sequence A093054 A093055 
               A093056
%K A093053 cofr,nonn
%O A093053 0,2
%A A093053 Paul D. Hanna (pauldhanna(AT)juno.com), Mar 16 2004