The glide of a number is defined as the number of iterations of the equation that are required before a number smaller than the original is reached. Glide records are set when a number's glide is larger than those of all the numbers that come before it. A list of records can be found at http://personal.computrain.nl/eric/wondrous/glidrecs.html. I've been calculating the "Odd Glides", essentially the same property, but with the even numbers removed. At least for the first million numbers the two sets are the same:
| Notice that all these numbers have remainder 3 when
divided by 4. |
[3, 5, 1]
[7, 11, 17, 13, 5]
[27, 41, 31, 47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23]
[703, 1055, 1583, 2375, 3563, 5345, 4009, 3007, 4511, 6767, 10151, 15227, 22841, 17131, 25697, 19273, 14455, 21683, 32525, 12197, 2287, 3431, 5147, 7721, 5791, 8687, 13031, 19547, 29321, 21991, 32987, 49481, 37111, 55667, 83501, 31313, 23485, 8807, 13211, 19817, 14863, 22295, 33443, 50165, 4703, 7055, 10583, 15875, 23813, 4465, 3349, 157]
[10087, 15131, 22697, 17023, 25535, 38303, 57455, 86183, 129275, 193913, 145435, 218153, 163615, 245423, 368135, 552203, 828305, 621229, 232961, 174721, 131041, 98281, 73711, 110567, 165851, 248777, 186583, 279875, 419813, 78715, 118073, 88555, 132833, 99625, 74719, 112079, 168119, 252179, 378269, 141851, 212777, 159583, 239375, 359063, 538595, 807893, 18935, 28403, 42605, 15977, 11983, 17975, 26963, 40445, 15167, 22751, 34127, 51191, 76787, 115181, 43193, 32395, 48593, 36445, 13667, 20501, 961]
[35655, 53483, 80225, 60169, 45127, 67691, 101537, 76153, 57115, 85673, 64255, 96383, 144575, 216863, 325295, 487943, 731915, 1097873, 823405, 308777, 231583, 347375, 521063, 781595, 1172393, 879295, 1318943, 1978415, 2967623, 4451435, 6677153, 5007865, 3755899, 5633849, 4225387, 6338081, 4753561, 3565171, 5347757, 2005409, 1504057, 1128043, 1692065, 1269049, 951787, 1427681, 1070761, 803071, 1204607, 1806911, 2710367, 4065551, 6098327, 9147491, 13721237, 643183, 964775, 1447163, 2170745, 1628059, 2442089, 1831567, 2747351, 4121027, 6181541, 1159039, 1738559, 2607839, 3911759, 5867639, 8801459, 13202189, 4950821, 928279, 1392419, 2088629, 195809, 146857, 110143, 165215, 247823, 371735, 557603, 836405, 78413, 29405]
[270271, 405407, 608111, 912167, 1368251, 2052377, 1539283, 2308925, 865847, 1298771, 1948157, 730559, 1095839, 1643759, 2465639, 3698459, 5547689, 4160767, 6241151, 9361727, 14042591, 21063887, 31595831, 47393747, 71090621, 26658983, 39988475, 59982713, 44987035, 67480553, 50610415, 75915623, 113873435, 170810153, 128107615, 192161423, 288242135, 432363203, 648544805, 121602151, 182403227, 273604841, 205203631, 307805447, 461708171, 692562257, 519421693, 194783135, 292174703, 438262055, 657393083, 986089625, 739567219, 1109350829, 416006561, 312004921, 234003691, 351005537, 263254153, 197440615, 296160923, 444241385, 333181039, 499771559, 749657339, 1124486009, 843364507, 1265046761, 948785071, 1423177607, 2134766411, 3202149617, 2401612213, 225151145, 168863359, 253295039, 379942559, 569913839, 854870759, 1282306139, 1923459209, 1442594407, 2163891611, 3245837417, 2434378063, 3651567095, 5477350643, 8216025965, 3081009737, 2310757303, 3466135955, 5199203933, 1949701475, 2924552213, 137088385, 102816289, 77112217, 57834163, 86751245, 32531717, 6099697, 4574773, 428885, 2513}
[362343, 543515, 815273, 611455, 917183, 1375775, 2063663, 3095495, 4643243, 6964865, 5223649, 3917737, 2938303, 4407455, 6611183, 9916775, 14875163, 22312745, 16734559, 25101839, 37652759, 56479139, 84718709, 7942379, 11913569, 8935177, 6701383, 10052075, 15078113, 11308585, 8481439, 12722159, 19083239, 28624859, 42937289, 32202967, 48304451, 72456677, 13585627, 20378441, 15283831, 22925747, 34388621, 12895733, 1208975, 1813463, 2720195, 4080293, 765055, 1147583, 1721375, 2582063, 3873095, 5809643, 8714465, 6535849, 4901887, 7352831, 11029247, 16543871, 24815807, 37223711, 55835567, 83753351, 125630027, 188445041, 141333781, 6625021, 2484383, 3726575, 5589863, 8384795, 12577193, 9432895, 14149343, 21224015, 31836023, 47754035, 71631053, 26861645, 10073117, 3777419, 5666129, 4249597, 1593599, 2390399, 3585599, 5378399, 8067599, 12101399, 18152099, 27228149, 2552639, 3828959, 5743439, 8615159, 12922739, 19384109, 7269041, 5451781, 1022209, 766657, 574993, 431245, 161717]
[381727, 572591, 858887, 1288331, 1932497, 1449373, 543515, 815273, 611455, 917183, 1375775, 2063663, 3095495, 4643243, 6964865, 5223649, 3917737, 2938303, 4407455, 6611183, 9916775, 14875163, 22312745, 16734559, 25101839, 37652759, 56479139, 84718709, 7942379, 11913569, 8935177, 6701383, 10052075, 15078113, 11308585, 8481439, 12722159, 19083239, 28624859, 42937289, 32202967, 48304451, 72456677, 13585627, 20378441, 15283831, 22925747, 34388621, 12895733, 1208975, 1813463, 2720195, 4080293, 765055, 1147583, 1721375, 2582063, 3873095, 5809643, 8714465, 6535849, 4901887, 7352831, 11029247, 16543871, 24815807, 37223711, 55835567, 83753351, 125630027, 188445041, 141333781, 6625021, 2484383, 3726575, 5589863, 8384795, 12577193, 9432895, 14149343, 21224015, 31836023, 47754035, 71631053, 26861645, 10073117, 3777419, 5666129, 4249597, 1593599, 2390399, 3585599, 5378399, 8067599, 12101399, 18152099, 27228149, 2552639, 3828959, 5743439, 8615159, 12922739, 19384109, 7269041, 5451781, 1022209, 766657, 574993, 431245, 161717]
[626331, 939497, 704623, 1056935, 1585403, 2378105, 1783579, 2675369, 2006527, 3009791, 4514687, 6772031, 10158047, 15237071, 22855607, 34283411, 51425117, 19284419, 28926629, 5423743, 8135615, 12203423, 18305135, 27457703, 41186555, 61779833, 46334875, 69502313, 52126735, 78190103, 117285155, 175927733, 16493225, 12369919, 18554879, 27832319, 41748479, 62622719, 93934079, 140901119, 211351679, 317027519, 475541279, 713311919, 1069967879, 1604951819, 2407427729, 1805570797, 677089049, 507816787, 761725181, 285646943, 428470415, 642705623, 964058435, 1446087653, 271141435, 406712153, 305034115, 457551173, 85790845, 32171567, 48257351, 72386027, 108579041, 81434281, 61075711, 91613567, 137420351, 206130527, 309195791, 463793687, 695690531, 1043535797, 97831481, 73373611, 110060417, 82545313, 61908985, 46431739, 69647609, 52235707, 78353561, 58765171, 88147757, 33055409, 24791557, 4648417, 3486313, 2614735, 3922103, 5883155, 8824733, 3309275, 4963913, 3722935, 5584403, 8376605, 3141227, 4711841, 3533881, 2650411, 3975617, 2981713, 2236285, 838607, 1257911, 1886867, 2830301, 1061363, 1592045, 597017}
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