mark9207 — "I didn't realize that there were clues in the brackets that would show up if you highlighted them with the cursor (I have no idea how to do that ..."To print a white font on a white background, use ☟ this is a white font on a white background ☚ highlight to make visible
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mark9207 — "I don't understand the "immediate company they keep" hint."That was my poor attempt at being subtle.
WARNING! SOLUTION ALERT! Highlight to see give-away hint below ☟
Each of the numbers in the sequence 4, 6, 12, …, 72, 102, … is bounded above and below by a pair of numbers that share a particular mathematical quality. For example, 12 is bounded by 11 and 13. Also, 72 is bounded by 71 and 73. The numbers 11, 13, 71, and 73 all share a unique feature. On the other hand, 78 is bounded by 77 and 79, one of which does not have this quality. WARNING OVER!
This numerical sequence is rather difficult. The sequence is covered in number theory, but that is usually given as a graduate course in pure mathematics. I don’t see how the average person could come up with a solution, as THE NUMBERS ARE NOT A FUNCTION OF PREVIOUS NUMBERS IN THE SERIES.
Finally, I have one bone to pick with the tappet brothers. As purportedly graduates of MIT, they should know that their list of numbers form a sequence, not a series. A series is the summation of a sequence, as in a power series, a Fourier series, or a Taylor’s series and so on. Perhaps an MIT degree should come with an expiration date.