Question: Seventy three, fifty six,...

We have the following sequence of natural numbers
1, 2, 4, 7, 11, 16, 67, 83, 46, 73, 47, 85, 70, 20, 16, 76, 83, 55, 73, 56, 85, 79, 119, 934, 463, 389, 1009, 9028, 8237, 7357, 7567, 7688, 8899, 10021, 12035, 53056, 65071, 17093, 39109, 90232, 23249, 94273, 37291, 19316, 61435, 53461, 16481, 18508, 80629, 92657, 75679, 97708, 80831, 13861, 16885, 58916, 62041, 14083, 38099, 99142, 24259, 95303, 30421, 12466, 66485, 58531, 13651, 15698, 89719, 91867, 76889, 98938, 84061, 16121, 12235, 53296, 69311, 11473, 37489, 98552, 25669, 96733, 33851, 15916, 62035, 53111, 11221, 12298, 89309, 90487, 78499, 99578, 87691, 19771, 17885, 58966, 67081, 18173, 37279, 97372, 27479, 97573, 37681, 18776, 67885, 58981, 19091, 19198, 89299, 99407, 70609, 90718, 81821, 12931, 14035, 53156, 65251, 15373, 37469, 96592, 29689, 98813, 32011, 11146, 64235, 53371, 17461, 16598, 89689, 98827, 73019, 91168, 86251, 15401, 10585, 58636, 63821, 12973, 38059, 95222, 22399, 99463, 36641, 14806, 60985, 59051, 15241, 14398, 89489, 98647, 74839, 93998, 90091, 19162, 26345, 54517, 71701, 10874, 47959, 96133, 33329, 92494, 49591, 19757, 75955, 56122, 22331, 13489, 98599, 99758, 85969, 97129, 92351, 15502, 20725, 52877, 78001, 10264, 46379, 97543, 34759, 95924, 43141, 14317, 71525, 52702, 20911, 12089, 98209, 90478, 87599, 99769, 96991, 20162, 26296, 69457, 75692, 29854, 46090, 9263, 3829, 9484, 5051, 1708, 8275, 5933, 3601, 1270, 929, 1138, 8521, 1469, 9853, 3802, 2297, 8137, 7534, 4574, 4972, 3013, 3323, 3454, 4765, 5897, 8209, 9253, 3755, 5800, 313, 542, 475, 805, 740, 280, 316, 848, 1084, 5038, 8543, 3697, 8203, 3269, 9865, 5932, 2639, 9607, 7315, 5384, 5083, 4054, 4754, 4825, 5536, 6608, 8320, 493, 650, 313, 571, 434, 694, 757, 1019, 9364, 4903, 3359, 9799, 10246, 64469, 96715, 52039, 93296, 69511, 11869, 97085, 58354, 45661, 16931, 14239, 93520, 2819, 9463, 3931, 1676, 7045, 5692, 3251, 1810, 469, 1253, 3811, 1474, 5033, 3598, 9247, 7724, 4573, 4051, 1802, 2380, 1132, ... .
 What is the next term? Is it possible to find that with Maple? The Lagrange polynomial is not taken into account. I'd like to recall a great answer by Carl Love to a similar question.  However, the current situation seems to be different. The Predict command of Mma fails here.