Algorithms based on number base systems?
I've noticed recently that there are a great many algorithms out there based in part or in whole on clever uses of numbers in creative bases.  For example:

- Binomial heaps are based on binary numbers, and the more complex skew binomial heaps are based on skew binary numbers.
- Some algorithms for generating lexicographically ordered permutations are based on the factoradic number system.
- Tries can be thought of as trees that look at one digit of the string at a time, for an appropriate base.
- Huffman encoding trees are designed to have each edge in the tree encode a zero or one in some binary representation.
- Fibonacci coding is used in Fibonacci search and to invert certain types of logarithms.

My question is: **what other algorithms are out there that use a clever number system as a key step of their intuition or proof?**. I'm thinking about putting together a talk on the subject, so the more examples I have to draw from, the better.

Thanks so much!
Algorithms based on number base systems?
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I've noticed recently that there are a great many algorithms out there based in part or in whole on clever uses of numbers in creative bases.  For example:

- Binomial heaps are based on binary numbers, and the more complex skew binomial heaps are based on skew binary numbers.
- Some algorithms for generating lexicographically ordered permutations are based on the factoradic number system.
- Tries can be thought of as trees that look at one digit of the string at a time, for an appropriate base.
- Huffman encoding trees are designed to have each edge in the tree encode a zero or one in some binary representation.
- Fibonacci coding is used in Fibonacci search and to invert certain types of logarithms.

My question is: **what other algorithms are out there that use a clever number system as a key step of their intuition or proof?**. I'm thinking about putting together a talk on the subject, so the more examples I have to draw from, the better.

Thanks so much!