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# Tag Archives: hyperbinary

## The hyperbinary sequence and the Calkin-Wilf tree

And now, the amazing conclusion to this series of posts on Neil Calkin and Herbert Wilf’s paper, Recounting the Rationals, and the answers to all the questions about the hyperbinary sequence. Hold on to your hats! The Calkin-Wilf Tree First, … Continue reading

Posted in arithmetic, computation, induction, iteration, number theory, pattern, proof, recursion, sequences, solutions
Tagged algorithm, binary, Calkin-Wilf, Euclidean, Haskell, hyperbinary, tree
6 Comments

## Hyperbinary conjecture seeking proof for a good time, long walks on the beach

Here’s the latest progress on the hyperbinary sequence. We’re trying to figure out the inverse relation of the function : given a particular number , where does it occur in the hyperbinary sequence? That is, what are the values of … Continue reading

Posted in challenges, pattern, people, proof, sequences
Tagged Euler, hyperbinary, inverse relation, totient
4 Comments

## More hyperbinary fun

When I originally posed Challenge #12, a certain Dave posted a series of comments with some explorations and partial solutions to part II (the hyperbinary sequence). Although I gave the “solution” in my last post, no solution to any problem … Continue reading

Posted in challenges, induction, pattern, proof, recursion, sequences, solutions
Tagged hyperbinary, induction
12 Comments

## Challenge #12 solution, part II

Yes, that’s right, that Challenge #12, posted one year, five months, and a day ago. You see, I have this nasty habit of starting things and not finishing them… well, better late than never! Question two of the aforementioned challenge … Continue reading

Posted in challenges, counting, induction, pattern, sequences, solutions
Tagged binary, hyperbinary
15 Comments