files / problems / two-smooth-summands / compute / certs / f_exceptions.json
{
"exceptions_0.4": [
{
"n": 3,
"F": 2,
"a": 1,
"b": 2,
"n^0.4": 1.5518455739153598,
"fails": true
},
{
"n": 4,
"F": 2,
"a": 2,
"b": 2,
"n^0.4": 1.7411011265922482,
"fails": true
},
{
"n": 5,
"F": 2,
"a": 1,
"b": 4,
"n^0.4": 1.9036539387158786,
"fails": true
},
{
"n": 7,
"F": 3,
"a": 1,
"b": 6,
"n^0.4": 2.17790642448278,
"fails": true
},
{
"n": 11,
"F": 3,
"a": 2,
"b": 9,
"n^0.4": 2.6094986352788734,
"fails": true
},
{
"n": 13,
"F": 3,
"a": 1,
"b": 12,
"n^0.4": 2.789827435889086,
"fails": true
},
{
"n": 14,
"F": 3,
"a": 2,
"b": 12,
"n^0.4": 2.8737647560281374,
"fails": true
},
{
"n": 15,
"F": 3,
"a": 3,
"b": 12,
"n^0.4": 2.9541769390627777,
"fails": true
},
{
"n": 23,
"F": 5,
"a": 3,
"b": 20,
"n^0.4": 3.5050251165172894,
"fails": true
},
{
"n": 46,
"F": 5,
"a": 1,
"b": 45,
"n^0.4": 4.624908368702249,
"fails": true
},
{
"n": 47,
"F": 5,
"a": 2,
"b": 45,
"n^0.4": 4.664865679718495,
"fails": true
},
{
"n": 53,
"F": 5,
"a": 3,
"b": 50,
"n^0.4": 4.894522709071677,
"fails": true
},
{
"n": 71,
"F": 7,
"a": 1,
"b": 70,
"n^0.4": 5.501781510642736,
"fails": true
},
{
"n": 119,
"F": 7,
"a": 7,
"b": 112,
"n^0.4": 6.764236515567794,
"fails": true
},
{
"n": 311,
"F": 11,
"a": 3,
"b": 308,
"n^0.4": 9.93354253181874,
"fails": true
},
{
"n": 479,
"F": 13,
"a": 11,
"b": 468,
"n^0.4": 11.806854338404632,
"fails": true
}
],
"all_0.4_really_fail": true,
"exceptions_1_3": [
{
"n": 3,
"F": 2,
"a": 1,
"b": 2,
"n^{1/3}": 1.4422495703074083,
"fails": true
},
{
"n": 4,
"F": 2,
"a": 2,
"b": 2,
"n^{1/3}": 1.5874010519681994,
"fails": true
},
{
"n": 5,
"F": 2,
"a": 1,
"b": 4,
"n^{1/3}": 1.7099759466766968,
"fails": true
},
{
"n": 6,
"F": 2,
"a": 2,
"b": 4,
"n^{1/3}": 1.8171205928321397,
"fails": true
},
{
"n": 7,
"F": 3,
"a": 1,
"b": 6,
"n^{1/3}": 1.912931182772389,
"fails": true
},
{
"n": 8,
"F": 2,
"a": 4,
"b": 4,
"n^{1/3}": 2.0,
"fails": false
},
{
"n": 11,
"F": 3,
"a": 2,
"b": 9,
"n^{1/3}": 2.2239800905693152,
"fails": true
},
{
"n": 13,
"F": 3,
"a": 1,
"b": 12,
"n^{1/3}": 2.3513346877207573,
"fails": true
},
{
"n": 14,
"F": 3,
"a": 2,
"b": 12,
"n^{1/3}": 2.4101422641752297,
"fails": true
},
{
"n": 15,
"F": 3,
"a": 3,
"b": 12,
"n^{1/3}": 2.46621207433047,
"fails": true
},
{
"n": 19,
"F": 3,
"a": 1,
"b": 18,
"n^{1/3}": 2.668401648721945,
"fails": true
},
{
"n": 21,
"F": 3,
"a": 3,
"b": 18,
"n^{1/3}": 2.7589241763811203,
"fails": true
},
{
"n": 22,
"F": 3,
"a": 4,
"b": 18,
"n^{1/3}": 2.802039330655387,
"fails": true
},
{
"n": 23,
"F": 5,
"a": 3,
"b": 20,
"n^{1/3}": 2.8438669798515654,
"fails": true
},
{
"n": 25,
"F": 3,
"a": 1,
"b": 24,
"n^{1/3}": 2.924017738212866,
"fails": true
},
{
"n": 26,
"F": 3,
"a": 2,
"b": 24,
"n^{1/3}": 2.9624960684073702,
"fails": true
},
{
"n": 27,
"F": 3,
"a": 3,
"b": 24,
"n^{1/3}": 3.0,
"fails": false
},
{
"n": 46,
"F": 5,
"a": 1,
"b": 45,
"n^{1/3}": 3.583047871015946,
"fails": true
},
{
"n": 47,
"F": 5,
"a": 2,
"b": 45,
"n^{1/3}": 3.6088260801386944,
"fails": true
},
{
"n": 53,
"F": 5,
"a": 3,
"b": 50,
"n^{1/3}": 3.756285754221072,
"fails": true
},
{
"n": 61,
"F": 5,
"a": 1,
"b": 60,
"n^{1/3}": 3.936497183102173,
"fails": true
},
{
"n": 69,
"F": 5,
"a": 5,
"b": 64,
"n^{1/3}": 4.101565929702347,
"fails": true
},
{
"n": 71,
"F": 7,
"a": 1,
"b": 70,
"n^{1/3}": 4.140817749422853,
"fails": true
},
{
"n": 77,
"F": 5,
"a": 2,
"b": 75,
"n^{1/3}": 4.254320865115005,
"fails": true
},
{
"n": 79,
"F": 5,
"a": 4,
"b": 75,
"n^{1/3}": 4.290840427026207,
"fails": true
},
{
"n": 92,
"F": 5,
"a": 2,
"b": 90,
"n^{1/3}": 4.514357435474001,
"fails": true
},
{
"n": 94,
"F": 5,
"a": 4,
"b": 90,
"n^{1/3}": 4.546835943776344,
"fails": true
},
{
"n": 95,
"F": 5,
"a": 5,
"b": 90,
"n^{1/3}": 4.562902635386966,
"fails": true
},
{
"n": 101,
"F": 5,
"a": 1,
"b": 100,
"n^{1/3}": 4.657009507803835,
"fails": true
},
{
"n": 103,
"F": 5,
"a": 3,
"b": 100,
"n^{1/3}": 4.687548147653597,
"fails": true
},
{
"n": 106,
"F": 5,
"a": 6,
"b": 100,
"n^{1/3}": 4.732623491163368,
"fails": true
},
{
"n": 107,
"F": 5,
"a": 27,
"b": 80,
"n^{1/3}": 4.7474593985234,
"fails": true
},
{
"n": 115,
"F": 5,
"a": 15,
"b": 100,
"n^{1/3}": 4.862944131094279,
"fails": true
},
{
"n": 119,
"F": 7,
"a": 7,
"b": 112,
"n^{1/3}": 4.9186847344587274,
"fails": true
},
{
"n": 121,
"F": 5,
"a": 1,
"b": 120,
"n^{1/3}": 4.9460874432487,
"fails": true
},
{
"n": 122,
"F": 5,
"a": 2,
"b": 120,
"n^{1/3}": 4.9596756638423,
"fails": true
},
{
"n": 125,
"F": 5,
"a": 5,
"b": 120,
"n^{1/3}": 4.999999999999999,
"fails": true
},
{
"n": 142,
"F": 7,
"a": 2,
"b": 140,
"n^{1/3}": 5.217103446276167,
"fails": true
},
{
"n": 191,
"F": 7,
"a": 2,
"b": 189,
"n^{1/3}": 5.758965220492401,
"fails": true
},
{
"n": 211,
"F": 7,
"a": 1,
"b": 210,
"n^{1/3}": 5.953341813139051,
"fails": true
},
{
"n": 213,
"F": 7,
"a": 3,
"b": 210,
"n^{1/3}": 5.972092619826399,
"fails": true
},
{
"n": 223,
"F": 7,
"a": 7,
"b": 216,
"n^{1/3}": 6.064126994506963,
"fails": true
},
{
"n": 238,
"F": 7,
"a": 14,
"b": 224,
"n^{1/3}": 6.197154434741126,
"fails": true
},
{
"n": 239,
"F": 7,
"a": 14,
"b": 225,
"n^{1/3}": 6.205821794895751,
"fails": true
},
{
"n": 284,
"F": 7,
"a": 4,
"b": 280,
"n^{1/3}": 6.5731384514424285,
"fails": true
},
{
"n": 299,
"F": 7,
"a": 5,
"b": 294,
"n^{1/3}": 6.686883076988654,
"fails": true
},
{
"n": 311,
"F": 11,
"a": 3,
"b": 308,
"n^{1/3}": 6.775168952273312,
"fails": true
},
{
"n": 319,
"F": 7,
"a": 4,
"b": 315,
"n^{1/3}": 6.832771452246442,
"fails": true
},
{
"n": 479,
"F": 13,
"a": 11,
"b": 468,
"n^{1/3}": 7.82429418587908,
"fails": true
},
{
"n": 551,
"F": 11,
"a": 1,
"b": 550,
"n^{1/3}": 8.198175283056287,
"fails": true
},
{
"n": 619,
"F": 11,
"a": 3,
"b": 616,
"n^{1/3}": 8.52243209752116,
"fails": true
},
{
"n": 622,
"F": 11,
"a": 6,
"b": 616,
"n^{1/3}": 8.53617797956334,
"fails": true
},
{
"n": 671,
"F": 11,
"a": 11,
"b": 660,
"n^{1/3}": 8.754691361801425,
"fails": true
},
{
"n": 719,
"F": 11,
"a": 15,
"b": 704,
"n^{1/3}": 8.958658121750135,
"fails": true
},
{
"n": 839,
"F": 11,
"a": 14,
"b": 825,
"n^{1/3}": 9.431642272283662,
"fails": true
},
{
"n": 851,
"F": 11,
"a": 4,
"b": 847,
"n^{1/3}": 9.476395693435768,
"fails": true
},
{
"n": 933,
"F": 11,
"a": 9,
"b": 924,
"n^{1/3}": 9.771484510176279,
"fails": true
},
{
"n": 937,
"F": 11,
"a": 55,
"b": 882,
"n^{1/3}": 9.785428852333746,
"fails": true
},
{
"n": 958,
"F": 13,
"a": 13,
"b": 945,
"n^{1/3}": 9.857992945359124,
"fails": true
},
{
"n": 1102,
"F": 11,
"a": 2,
"b": 1100,
"n^{1/3}": 10.329053609850474,
"fails": true
},
{
"n": 1103,
"F": 11,
"a": 3,
"b": 1100,
"n^{1/3}": 10.332177000911681,
"fails": true
},
{
"n": 1117,
"F": 11,
"a": 28,
"b": 1089,
"n^{1/3}": 10.375707601615272,
"fails": true
},
{
"n": 1151,
"F": 13,
"a": 7,
"b": 1144,
"n^{1/3}": 10.47993143322853,
"fails": true
},
{
"n": 1193,
"F": 11,
"a": 5,
"b": 1188,
"n^{1/3}": 10.605882577922875,
"fails": true
},
{
"n": 1238,
"F": 11,
"a": 6,
"b": 1232,
"n^{1/3}": 10.737591595966624,
"fails": true
},
{
"n": 1244,
"F": 11,
"a": 12,
"b": 1232,
"n^{1/3}": 10.754910322100939,
"fails": true
},
{
"n": 1291,
"F": 11,
"a": 11,
"b": 1280,
"n^{1/3}": 10.888684494906176,
"fails": true
},
{
"n": 1319,
"F": 13,
"a": 32,
"b": 1287,
"n^{1/3}": 10.966842300729972,
"fails": true
},
{
"n": 1437,
"F": 13,
"a": 7,
"b": 1430,
"n^{1/3}": 11.284584927542857,
"fails": true
},
{
"n": 1559,
"F": 17,
"a": 12,
"b": 1547,
"n^{1/3}": 11.595301307469718,
"fails": true
},
{
"n": 1679,
"F": 13,
"a": 15,
"b": 1664,
"n^{1/3}": 11.88548473818796,
"fails": true
},
{
"n": 1916,
"F": 13,
"a": 5,
"b": 1911,
"n^{1/3}": 12.420292821573119,
"fails": true
},
{
"n": 2999,
"F": 17,
"a": 7,
"b": 2992,
"n^{1/3}": 14.420893025463036,
"fails": true
},
{
"n": 3071,
"F": 17,
"a": 11,
"b": 3060,
"n^{1/3}": 14.535387209845743,
"fails": true
},
{
"n": 3118,
"F": 17,
"a": 24,
"b": 3094,
"n^{1/3}": 14.609164197154643,
"fails": true
},
{
"n": 4677,
"F": 17,
"a": 2,
"b": 4675,
"n^{1/3}": 16.72331832828313,
"fails": true
},
{
"n": 5711,
"F": 19,
"a": 11,
"b": 5700,
"n^{1/3}": 17.874643414732805,
"fails": true
},
{
"n": 10559,
"F": 23,
"a": 2,
"b": 10557,
"n^{1/3}": 21.938533661789428,
"fails": true
},
{
"n": 18191,
"F": 29,
"a": 8,
"b": 18183,
"n^{1/3}": 26.29978458381583,
"fails": true
}
],
"all_1_3_really_fail": false,
"spot_nonlisted": [
{
"n": 480,
"F": 3,
"n^0.4": 11.81670775625111,
"ok04": true,
"n^{1/3}": 7.829735282337726,
"ok13": true
},
{
"n": 481,
"F": 5,
"n^0.4": 11.82654886500849,
"ok04": true,
"n^{1/3}": 7.835168826956221,
"ok13": true
},
{
"n": 500,
"F": 5,
"n^0.4": 12.011244339814313,
"ok04": true,
"n^{1/3}": 7.937005259840997,
"ok13": true
},
{
"n": 1000,
"F": 5,
"n^0.4": 15.848931924611136,
"ok04": true,
"n^{1/3}": 9.999999999999998,
"ok13": true
},
{
"n": 1559,
"F": 17,
"n^0.4": 18.929469634297398,
"ok04": true,
"n^{1/3}": 11.595301307469718,
"ok13": false
},
{
"n": 3496,
"F": 5,
"n^0.4": 26.147403543720827,
"ok04": true,
"n^{1/3}": 15.177158675563629,
"ok13": true
},
{
"n": 10000,
"F": 5,
"n^0.4": 39.810717055349734,
"ok04": true,
"n^{1/3}": 21.544346900318832,
"ok13": true
},
{
"n": 480,
"F": 3,
"n^0.4": 11.81670775625111,
"ok04": true,
"n^{1/3}": 7.829735282337726,
"ok13": true
}
],
"is_dent": false,
"reason": "Finite exception lists for F(n)<=n^alpha on a prefix. Not an infinite covering."
}