[seqfan] Re: A098550.

[Hans Havermann]

> By the way, if we iterate n -> A098550(n), I have yet to find a longer loop than (1470, 2031, 1882, 1742, 2145, 1986, 2353, 5455, 6241, 2917, 2706, 2516, 2334, 2164, 2008, 1862, 2259, 2737, 2542, 3105, 3749, 3480, 4155, 3868, 3602, 4287, 1997, 1852, 1716, 1592).

Here's a length-84 loop to supersede that length-30 one:

(1772, 2167, 2697, 3193, 2970, 2758, 3303, 3939, 4665, 5525, 12895, 15043, 17367, 19673, 18534, 21289, 20072, 18912, 17812, 20545, 19348, 18230, 20987, 29661, 33885, 39055, 44439, 42080, 47875, 54307, 25741, 12149, 11400, 10704, 10042, 11603, 13545, 12724, 14757, 16867, 19523, 18394, 17316, 19901, 18752, 17660, 20363, 23451, 11059, 12643, 11878, 11156, 10472, 9822, 11487, 10782, 5059, 6015, 5614, 6655, 6224, 5810, 6853, 6416, 7571, 10623, 12293, 11548, 10844, 12609, 11842, 13797, 12964, 15051, 17379, 16400, 7717, 7218, 6754, 3163, 3741, 4399, 4106, 1913)


Neil Sloane:

> What about the following related sequences:
> - length of loop if you start at n

Alas, 11 already is unresolved. It is part of a chain that may be extended in either direction (reminding me of my long-ago A038807 - except A098550 chains appear to be somewhat more tractable):

(..., 365567, 349678, 385717, 184511, 206371, 196920, 187866, 89599, 85156, 95637, 107191, 101970, 114109, 108602, 121627, 136249, 152305, 145110, 138252, 154341, 172071, 191687, 182848, 203541, 194206, 216067, 239867, 266205, 254300, 242882, 269521, 257466, 245914, 234840, 112111, 125757, 119722, 113954, 108448, 121425, 135835, 129372, 144537, 137708, 131168, 146485, 164107, 156434, 149092, 166299, 158536, 151106, 143986, 160689, 153160, 145954, 139058, 155199, 173147, 192741, 183874, 87683, 83330, 79176, 88933, 99861, 94974, 106473, 119211, 133357, 126990, 141903, 158367, 176535, 196267, 218169, 242351, 269005, 128489, 122338, 136775, 152709, 72763, 81991, 92065, 103385, 98342, 93518, 44453, 42098, 19927, 22953, 21646, 20404, 19228, 22149, 20882, 19674, 22471, 21194, 24405, 27985, 31553, 36055, 34092, 32226, 36751, 17383, 16364, 15390, 14472, 16815, 15816, 14890, 14002, 13160, 12364, 14331, 16551, 7789, 9135, 8564, 10023, 11747, 13571, 12740, 11972, 5623, 5254, 6183, 2887, 2680, 3231, 3004, 3553, 3308, 3080, 2866, 3415, 4075, 4873, 2273, 2106, 1950, 1808, 2171, 2533, 2350, 2779, 3403, 3162, 2942, 1367, 1260, 1168, 1445, 1342, 1659, 1532, 1418, 1757, 1620, 1500, 691, 317, 391, 362, 334, 308, 284, 252, 230, 299, 278, 369, 344, 423, 193, 259, 319, 425, 579, 759, 349, 318, 294, 274, 127, 59, 87, 41, 38, 91, 88, 43, 19, 27, 28, 51, 23, 13, 35, 34, 55, 75, 72, 133, 120, 195, 182, 166, 209, 192, 178, 156, 146, 205, 180, 162, 219, 295, 371, 342, 471, 420, 595, 763, 963, 443, 543, 753, 1023, 940, 1195, 1106, 509, 470, 583, 528, 241, 222, 103, 329, 151, 142, 67, 68, 77, 74, 161, 148, 215, 101, 47, 57, 81, 111, 153, 71, 60, 62, 31, 18, 20, 22, 11*, 25, 26, 45, 95, 78, 105, 203, 196, 267, 455, 424, 392, 555, 498, 440, 406, 376, 340, 785, 1025, 944, 880, 1119, 1036, 1363, 1715, 2097, 2369, 1097, 1385, 641, 801, 730, 672, 867, 1077, 1341, 1238, 1713, 2091, 971, 1169, 541, 251, 339, 312, 288, 264, 242, 305, 413, 481, 1115, 1030, 1247, 1152, 1391, 1643, 2023, 1872, 1736, 2133, 2561, 2376, 2204, 2667, 2472, 2923, 2716, 13849, 16053, 18549, 21181, 19964, 22411, 21134, 24305, 11467, 10770, 10104, 11757, 13663, 15529, 17821, 16786, 19247, 22183, 25515, 36123, 34162, 39049, 44391, 50367, 47726, 45214, 42812, 40530, 46145, 52597, 49854, 56497, 53568, 60609, 68453, 64980, 73311, 69600, 78481, 88197, 99015, 111009, 124275, 118284, 132227, 147705, 164841, 157142, 149766, 142716, 159173, 177405, 197417, 188334, 449105, 495055, 545313, 600955, 575892, 275897, 131797, 62753, 59536, 67461, 76433, 72596, 68924, 65424, 62092, 58898, 66259, 62888, 89499, 100443, 95524, 90820, 86324, 96965, 108765, 121749, 289735, 320773, 306652, 339435, 374707, 358448, 396215, 379092, 362658, 400865, 383564, 366954, 351014, 387981, 371194, 355078, 392525, 433353, 477885, 457568, 438036, 419278, 462403, 509617, 488076, 467368, 447450, 493227, 543279, 520434, 498456, 477352, 457060, 503741, 554647, 531366, 508976, 560713, 616847, ...)