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STL comments on An Intuitive Explanation of Solomonoff Induction - Less Wrong
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Here is my favorite integer sequence:
Arrange N points around a circle, then draw lines between all of them in order to slice up the circle. What is the maximum number of regions that you can obtain?
N=1 gives you 1 region (the whole circle). N=2 gives you 2 regions (a single cut) N=3 gives you 4 regions (a triangle and 3 circular segments). N=4 gives you 8 regions (a quadrilateral with an X gives you 4 triangles and 4 circular segments).
Remember, these are the maximum numbers - I have provided examples of how to get them, but there is no way to get more regions. (Obvious for low N, harder to prove for higher N.)
What are the next two numbers?
Answer: http://oeis.org/A000127
I was one asked the answer to that with N=6. I noticed the pattern for N <= 5, but I suspected they were trying to trick me so I actually tried to determine it from scratch. (As for the “Obvious for low N, harder to prove for higher N” part, I used the heuristic that if no three of the lines met at one same point inside the circle, I had probably achieved the maximum. It worked.)
OTOH I was once asked "2, 3, 5, 7, what comes next?" and I immediately answered “that's the prime numbers, so it's 11”, but there was some other sequence they were thinking about (I can't remember which).
At least those
Yes, the OEIS is a great way to learn first-hand the Strong Law of Small Numbers. This sequence being a particularly nice example of "2,3,5,7,11,?".