Tag Archives: hyperbinary

The hyperbinary sequence and the Calkin-Wilf tree

Posted on October 18, 2009 by Brent

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 , , , , , , | 6 Comments

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

Posted on October 12, 2009 by Brent

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 , , , | 4 Comments

More hyperbinary fun

Posted on September 28, 2009 by Brent

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 , | 12 Comments

Challenge #12 solution, part II

Posted on September 19, 2009 by Brent

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 , | 15 Comments