Sloane's Gap - Numberphile

Background on the On-Line Encyclopedia of Integer Sequences: [LINK] Very good video on Sloane's Gap, for the impatient: [VIDEO] The article is particularly interesting to me for it's examination of what complexity theory tells us to expect for the distribution of 'interesting' integer sequences. That cultural influences can (probably) have such a dramatic and measurable effect on something like mathematics is fascinating as well.

Well the first number that doesn't appear in OEIS is 18159. That make it interesting to me , but apparently this number isn't interesting to mathematicians. Of course since OEIS is finite, there will always be numbers which don't make it. What's really interesting is that some numbers are disproportionately underrepresented. They appear much less often than other numbers of the same size. And if you plot each number by the number of times it occurs, it makes a really interesting pattern: [VIDEO]

When you plot the "importance" N(n) of the positive integers, where N(n) = The number of occurrences of n in the OEIS an interesting anomaly appears[1]. The "importance" of the integers fall into two clusters, separated by Sloane's Gap [2][3]. Also, Neil Sloane appeared[4] several times on Numberphile. In the last few videos of that[4] playlist ("Amazing Graphs"), Sloane shares some of the particularly interesting sequences from the OEIS. [1] [LINK] [2] [LINK] [3] [VIDEO] [4] [LINK]