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Numerators of the Collatz parity generator fractions.
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%I #8 Aug 27 2017 23:44:19

%S 1,3,7,191,25983,2663063519,7160414743310596607,

%T 208229791652776621349215306687873023871,

%U 45218742589363955614633859184750699518167124046103786511727246869388335095775

%N Numerators of the Collatz parity generator fractions.

%C a(n) is a numerator of a fraction of the form a(n)/(2^2^n + 1) whose expansion into a repeating binary string models the n-th parity in the Collatz orbit of an integer.

%e a(1)=1 => f(1) = 1/3 => b(1) = 101010...

%e a(2)=3 => f(2) = 3/5 => b(2) = 10011001...

%e elements in b(2) determine the parity of elements at index 2 in the Collatz parity sequence of an integer.

%Y Cf. A006666.

%K nonn

%O 1,2

%A _John Laky_, Aug 22 2017