Category Archives: sequences

Open problems: Collatz conjecture

Posted on May 8, 2007 by Brent

Pick any integer you like. Got an integer? OK, now apply this simple rule: if the integer is even, divide by two; otherwise, multiply by three and add one. For example, if you started with 10, you would get 5; … Continue reading →

Posted in iteration, open problems, sequences | 33 Comments

Triangular number formula (Challenge #8)

Posted on February 12, 2007 by Brent

More hosting issues recently… sigh. I’m seriously considering moving TMLT to a different hosting provider… the only problem being that right now, my hosting is free, and it might be hard to find another host which provides all the tools … Continue reading →

Posted in challenges, computation, famous numbers, sequences | 12 Comments

Computing tetrahedral numbers

Posted on December 22, 2006 by Brent

I left off the discussion of tetrahedral numbers in my last post by posing the question of what the 144th tetrahedral number is, and promising to explain a quick way to figure it out without having to actually add up … Continue reading →

Posted in computation, famous numbers, geometry, sequences | 3 Comments

The Twelve Days of Christmas and Tetrahedral Numbers

Posted on December 20, 2006 by Brent

(Edit, 12/5/07: I guess it’s that time of year again, isn’t it? =) I’ve started to see a lot more traffic to this post in the last few days. For anyone finding me through a Google search, I wanted to … Continue reading →

Posted in famous numbers, games, geometry, sequences | 17 Comments

Challenge #4 Solution, Part II

Posted on July 7, 2006 by Brent

But wait! What happened to Part I, you ask!? Well, let’s play the Multiple Choice Game! (a) There is no Part I. (b) There USED to be a Part I, but it disappeared. (c) Part I will come later. Haven’t … Continue reading →

Posted in sequences, solutions | Comments Off on Challenge #4 Solution, Part II

Challenge #4

Posted on May 3, 2006 by Brent

Another sequence-related challenge for your sequencing pleasure. For those of you in my Elementary Functions class, this is extra credit. (Hence, if you post a comment with your solutions, please refrain from posting an explanation along with it.) Find the … Continue reading →

Posted in challenges, sequences | 1 Comment

Challenge #3 Solution

Posted on April 28, 2006 by Brent

Solutions to Challenge #3 follow. If you absolutely must read the solutions without attempting the challenge, I certainly can’t stop you. But Santa Claus knows.

Posted in sequences, solutions | 2 Comments

Challenge #3

Posted on April 22, 2006 by Brent

It’s been a little while since my last post… I plead spring break vacation. At any rate, hopefully you figured out that the last post was intended as an April Fool’s joke. I hope you didn’t embarass yourself too badly … Continue reading →

Posted in challenges, sequences | 2 Comments