In the OEIS’ search engine, you must use more than a few terms of an unknown sequence. After all, how many sequences start with 0, 1, 2, ...?
So the numbers 0 and 1 are highly popular since they appear in lots of sequences. Essentially, if a number has some interesting property, it might be in a sequence of integers. The more interesting properties it has, the more sequences it might appear in.
So in 2008 Philippe Guglielmetti wondered about “uninteresting numbers” that aren’t part of any sequence in the OEIS^{1}. Back then 8795 was the smallest one.
Then in 2009, Dr. Guglielmetti and JeanPaul Delahaye wondered about how many sequences does any particular number appear in. When plotted, it became apparent that there were two groups of numbers, dubbed “interesting” and “uninteresting”, with a clear gap between them.
This was dubbed Sloane’s Gap. The divide might be interpreted as a social effect rather than an intrinsic, objective mathematical fact (Gauvrit, Delahaye, and Zenil 2011; Forgues, Guglielmetti, and McEachen 2011).
Half your age plus seven ← Andy’s Brevity Quest 2019 (247 words) → Bacon jam
References
Forgues, Daniel, Philippe Guglielmetti, and Bill McEachen. 2011. “Frequency of Appearance in the Oeis Database.” Edited by The OEIS Wiki editors. October 8, 2011. https://oeis.org/w/index.php?title=Frequency_of_appearance_in_the_OEIS_database&oldid=1618639.
Gauvrit, Nicolas, JeanPaul Delahaye, and Hector Zenil. 2011. “Sloane’s Gap. Mathematical and Social Factors Explain the Distribution of Numbers in the Oeis.” arXiv:1101.4470 [math.PR], January. http://arxiv.org/abs/1101.4470v2.

Excluding, of course, A000027↩︎