# Category Archives: sequences

## Open problems: Collatz conjecture

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)

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

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

(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

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

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

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

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