A291352 Numerators of the Collatz parity generator fractions.

1, 3, 7, 191, 25983, 2663063519, 7160414743310596607, 208229791652776621349215306687873023871, 45218742589363955614633859184750699518167124046103786511727246869388335095775

Offset: 1

Author

John Laky, Aug 22 2017

Keywords

• nonn

Comments

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.

Examples

			a(1)=1 => f(1) = 1/3 => b(1) = 101010...
a(2)=3 => f(2) = 3/5 => b(2) = 10011001...
elements in b(2) determine the parity of elements at index 2 in the Collatz parity sequence of an integer.
		

Crossrefs

Cf. A006666.