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 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. 1

%I

%S 1,2,5,11,23,46,93,186,372,745,1490,2980,5960,11921,23843,47686,95373,

%T 190746,381493,762986,1525973,3051946,6103893,12207787,24415575,

%U 48831150,97662301,195324602,390649204,781298409,1562596819,3125193638

%N 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 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 x=[1;2,5,11,23,46,93,186,372,745,1490,2980,5960,11921,23843,...].

%e x=1.455281692832971051393034444524589699271213777825554774132070945742167...

%p {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 Cf. A093054.

%K cofr,nonn

%O 0,2

%A _Paul D. Hanna_, Mar 16 2004

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Last modified June 18 12:23 EDT 2021. Contains 345106 sequences. (Running on oeis4.)