“Search the keyword “cloud,” for instance, and you get sequence A136281: Among the references you find the comment: “These are thunderstorm graphs. Their connected components are a single cycle (clouds), a path (lightning bolts), or an isolated vertex (raindrops).””
“Enter the keyword “sky” and you get sequence A074481 with the comment: “These primes form a pattern similar to an astronomical radiant (the point in the sky from which a meteor shower appears to originate).””
“Generally, anything that can be counted is fair game. Even philosophy itself. One such example, according to Charles Greathouse, an editor in chief and trustee of the encyclopedia’s foundation, and an analyst and programmer at Case Western Reserve University, “would be the debate between Hipparchus and Chrysippus about (according to Plutarch) the number of compound propositions, which the former gave as 103,049 or 310,954 and the latter as more than 1 million. It seems that Hipparchus was referring to sequences A001003 and A010683 and Chrysippus to A025225. All three are sequences about counting objects very much like what is described in the fragments which remain of those writers.””
“Start Counting: Sequence A25001 in the encyclopedia defines the number of ways to arrange any number of circles on the plane. There is one way to draw one circle, three ways to draw two circles, 14 ways to draw three circles, 173 ways to draw four circles (recently corrected from a previous count of 168), and a preliminary count predicts there are 16,968 ways to draw five circles.Jon Wild”
“It’s in this sense that a sequence is a fingerprint—a lingua franca or a barcode or canonical form—that can unlock the identity of a little known mathematical or scientific object, or objects and their hitherto unknown interconnectedness.”
“Ultimately, it all comes back to counting things, and counting is a universally handy tool. Which in turn makes the encyclopedia handy, too.”
“Gupta and his colleague, Nilay Chheda, cited the encyclopedia in their paper “RNA as Permutation,” which detailed a novel interpretation of RNA in an information-theoretic perspective. Without getting into the technical details, it’s easy to imagine how integer sequences might apply to genetics: A gene is a sequence of DNA, and a DNA sequence in turn defines an RNA sequence. The process of DNA sequencing determines the pattern or order of the AGCT nucleotide bases (adenine, guanine, cytosine, thymine). Researchers in this field, said Gupta, use “different mathematical objects such as graphs, groups, formal languages, and combinatorics. Each such representation gives rise to connections with numbers.” And the most famous connection, he said, is with a sequence of numbers known as the Catalan numbers, which of course has its entry in the encyclopedia, as sequence A004148.”