Participatory. Jenkins. 1729 (= 19 * 91) (= 1^3 + 12^3 = 9^3 + 10^3) on wikipedia. The two different ways are these: Of course, equating "smallest" with "most negative", as opposed to "closest to zero" gives rise to solutions like −91, −189, −1729, and further negative numbers.
This ambiguity is eliminated by the term "positive cubes". Essays: The Flypaper Sequence Mystery. By Michael Barrier An August 13, 2012, update: Gunnar Andreassen has written to me about the sketches below.
For background on just why these sketches, and others like them, have proved to be such frustrating puzzles, go to the original post below and work your way forward. Here is what Gunnar wrote: I just stumbled over some more drawings from this sequence, sold at auction by S/R Laboratories. David Bordwell. The nonist.