Thanks to Jon Ziegler's sharp eyes re << And especially 3. {4 (1), 8 (3), 24 (5), 90 (7), 114 (13), . . . } shows the first number of each new record-breaking (in length) run of composites followed by the (length) of this run. The latter sequence 1, 3, 5, 7, 13,... is A066963 in OEIS, . . .

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it's clear that << . . . but 4, 8, 24, 90, 114, . . . -- the first numbers of each such run -- does not seem to be there. is wrong: 4,8,24,90,114,... is indeed in OEIS as A008950 (with the same definition). (The midpoints of each record run: 4,9,26,93,120,... don't appear, though that's not too important.) --Dan