The Online Encyclopedia of Integer Sequences (OEIS) was founded in 1964 by Neil Sloane. It now encompasses a quarter-million sequences, and it is a phenomenal reference for anyone involved in math. This page makes connections between the OEIS and this Web site.
- McNuggets (OEIS: A214777).
If you can order 6, 9, or 20, what numbers can you NOT order? - This, and a generalization, appeared in Lesson 5.08 of Algebra: Themes, Tools, Concepts.
- Trapezoidal numbers (aka staircases):
- Which numbers can be written as the sum of consecutive positive integers? (OEIS: A057716)
- In how many ways? (OEIS: A069283)
- Polyforms are the shapes you get by combining multiple copies of a given "form" (usually a polygon,) attached to each other edge-to-edge. I discuss them, and link to many other pages, in Geometric Puzzles in the Classroom. Specifically:
- Pentominoes are polyominoes (OEIS: A000105).
- Supertangrams are polytans, aka polyaboloes (OEIS: A006074)
- And my own invention: polyarcs (OEIS: A057787)
- Polyomino perimeter (OEIS: A027709) is the subject of one of my all-time favorite lessons.
- Lessons 1.01 and 1.02 in Algebra: Themes, Tools, Concepts
- Labs 8.1 to 8.3 in Geometry Labs
- Square-Sum Pair Partitions: Arrange the whole numbers from 1 to 18 into nine pairs so that the sum of the numbers in each pair is a perfect square. Generalize. (OEIS: A253472)
- This article, co-authored with Gord Hamilton and Kiran Kedlaya won the MAA Polya Prize.
- Prime numbers: In my Infinity course, one of the units is about infinite sets, and includes:
- The proof that there are an infinite number of primes (OEIS: A000040)
- Slime numbers, i.e. concatenations of primes (OEIS: A166504, A085823)
- More sequences! Another unit in the same course is about proof by mathematical induction, and includes:
- Triangular numbers (OEIS: A000217)
- Centered pentagonal numbers (OEIS: A005891)
- Fibonacci numbers (OEIS: A000045)
- Sum of cubes (OEIS: A000537)