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For any nonnegative real number x, let f(x) be the real number obtained by replacing in the binary expansions of the integer and fractional parts of x each finite run of k consecutive equal bits b with a run of k-(-1)^k consecutive bits b; a(n) is the denominator of f(1/n).
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%I #9 Feb 27 2020 23:34:53

%S 1,4,5,16,3,5,7,8,17,24,257,20,129,56,21,64,9,17,1025,12,15,257,2047,

%T 10,8193,129,1025,28,10923,21,31,32,65,72,87381,68,2097153,8200,16383,

%U 96,2049,120,1025,1028,5461,16376,536870911,80,33554431,65544,1365,516

%N For any nonnegative real number x, let f(x) be the real number obtained by replacing in the binary expansions of the integer and fractional parts of x each finite run of k consecutive equal bits b with a run of k-(-1)^k consecutive bits b; a(n) is the denominator of f(1/n).

%H Rémy Sigrist, <a href="/A323627/a323627.gp.txt">PARI program for A323627</a>

%F a(2^k) = 2^(k+1+(-1)^k) for any k >= 2.

%o (PARI) See Links section.

%Y See A323626 for the corresponding numerators and additional comments.

%K nonn,frac,base

%O 1,2

%A _Rémy Sigrist_, Jan 20 2019