"There is no one way"

Sunday, July 19, 2015

Integer Sequences

Last winter, I attended an interesting meeting of mathematicians and math educators in Banff, Canada. Our charge was to compile a list of integer sequences that would offer suitable problems for students (and teachers) at each level from Kindergarten to 12th grade. It was a sequel to 2014's Unsolved K-12 meeting, and once again was organized by Gord Hamilton.

Integer sequences are of course hugely important in K-12 math, and I don't just mean arithmetic, geometric, and Fibonacci sequences. In fact, many of my favorite problems of many types and at all levels yield integer sequences. More generally, tens of thousands of problems in all areas of mathematics yield integer sequences. A quarter million integer sequences have been cataloged in the Online Encyclopedia of Integer Sequences (OEIS), a collection started in 1964 by Neil Sloane.

I only heard about it recently, and was amazed to find that many sequences I had "invented" (and that some of you may recognize from my various curriculum materials) had been posted there by other people. In fact, I was pleased and honored that Neil Sloane himself posted the sequence of the numbers of polyarcs, a topic from recreational math that I created some decades ago.

I did add a sequence to the OEIS myself, one that I was surprised was not on there yet — the answer to this question: "Partition the numbers from 1 to 2n into pairs, so that the sum of the numbers in each pair is a perfect square. For what numbers is this possible?" (For more on this question, see this blog post and its sequel.)

Anyway, the point of today's post is to let you know that I created a page of links to some K-12 activities on my site, and to the corresponding sequences on the OEIS. Check it out!


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