Author: peterkagey
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My Favorite Sequences: A263135
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This is the fourth in my installment of My Favorite Sequences. This post discusses sequence A263135 which counts penny-to-penny connections among \(n\) pennies on the vertices of a hexagonal grid. I published this sequence in October 2015 when I was thinking about hexagonal-grid analogs to the “Not Equal” grid. The square-grid analog of this sequence…
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My Favorite Sequences: “Not Equal” Grid
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This is the third installment in a recurring series, My Favorite Sequences. This post discusses OEIS sequence A278299, a sequence that took over two years to compute enough terms to add to the OEIS with confidence that it was distinct. This sequence is discussed in Problem #23 of my Open Problems Collection, which asks for…
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My Favorite Sequences: A289523
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This the second post in a recurring series, My Favorite Sequences. If you like this sort of thing, check out the Integer Sequence Review from The Aperiodical! A289523: Packing Circles of Increasing Area In July 2017, I added a mathematically-silly-but-visually-fun sequence, A289523. The sequence works like this: place a circle of area \(\pi\) centered at…
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My Favorite Sequences: A261865
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This is the first installment in a new series, “My Favorite Sequences”. In this series, I will write about sequences from the On-Line Encyclopedia of Integer Sequences that I’ve authored or spent a lot of time thinking about. I’ve been contributing to the On-Line Encyclopedia of Integer Sequences since I was an undergraduate. In December…
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Richard Guy’s Partition Sequence
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Neil Sloane is the founder of the On-Line Encyclopedia of Integer Sequences (OEIS). Every year or so, he gives a talk at Rutgers in which he discusses some of his favorite recent sequences. In 2017, he spent some time talking about a 1971 letter that he got from Richard Guy, and some questions that went…
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A π-estimating Twitter bot: Part III
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In the final part of this three-part series, I’ll give technical step-by-step instructions for how to wire up our Twitter bot, @BotfonsNeedles, to Docker and deploy it on the free tier of AWS Lambda, so that it can run until the end of time. I’ll also include some tips that I wish I knew when…
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A π-estimating Twitter bot: Part II
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This is the second part of a three part series about making the Twitter bot @BotfonsNeedles. Click here for Part I. In this part, I’ll explain how to use the Twitter API to post the images to Twitter via the Python library Tweepy, and keep track of all of the Tweets to get an increasingly…
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A π-estimating Twitter bot: Part I
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This is the first part of a three part series about making the Twitter bot @BotfonsNeedles. In this part, I will write a Python 3 program that uses a Monte Carlo method to approximate \(\pi\) with Buffon’s needle problem, and produces an image with the Python library Pillow In the second part, I’ll explain how…
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Polytopes with Lattice Coordinates
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Problems 21, 66, and 116 in my Open Problem Collection concern polytopes with lattice coordinates—that is, polygons, polyhedra, or higher-dimensional analogs with vertices the square or triangular grids. (In higher dimensions, I’m most interested in the \(n\)-dimensional integer lattice and the \(n\)-simplex honeycomb). This was largely inspired by one of my favorite mathematical facts: given…
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Parity Bitmaps from the OEIS
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My friend Alec Jones and I wrote a Python script that takes a two-dimensional sequence in the On-Line Encyclopedia of Integer Sequences and uses it to create a one-bit-per-pixel (1BPP) “parity bitmaps“. The program is simple: it colors a given pixel is black or white depending on whether the corresponding value is even or odd.…