Integer Sequences

Henri Picciotto

(Looking for arithmetic and geometric sequences? Click here.)

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. I will use this page to make 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)