True so far

Question (by me, Eric Angelini) was (minor typos deleted) :

> Hello Math-Fun and Seqfan,
>
> I've just sent this to the OEIS :

10 12 13 14 15 16 17 18 19 20 23 24 25 26 27 28 29 30
34 35 36 37 38 39 40 45 46 47 48 49 50 56 57 58 59 60
67 68 69 70 78 79 80 89 90 102 103 104 105 106 107
108 109 112 113 114 115 116 117 118 119 123 124 125
126 127 128 129 134 135 136 137 138 139 145 146 147
148 149 156 157 158 159 167 168 169 178 179 180 189...

> Description :

"True so far"-sequence. Last digit of a(n) must be seen
as a glyph and preceding digits as a quantity. So "10"
reads [one "0"] and "12" [one "2"] -- which are both true
statements: there is only one "0" glyph so far in the
sequence when [10] is read, and there is only one "2"
glyph when [12] is read. The sequence is built with
[a(n+1)-a(n)] being minimal and a(n+1) always "true so
far". This explains why integers [11], [21], [22], [31],
etc. are not in: their statements are false.

The nice substring ...1112,1113,1114,1115,1116,1117...
appears in the sequence -- which means that so far the
whole sequence has used 111 "2", 111 "3", 111 "4", 111 "5",
111 "6" and 111 "7"...

> Question which ruined my sleep tonight:
>
> Will the sequence ever stop?
>
> ... my intuition says yes...
> ... could someone compute this and check for some more integers?
>
> Thanks,
> É.

« True So far »

2024 terms computed by Chuck Seggelin, Feb. 22nd, 2005.

The sequence is finite.

10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 29, 30, 34, 35, 36, 37, 38, 39, 40, 45, 46, 47, 48, 49, 50, 56, 57, 58, 59, 60, 67, 68, 69, 70, 78, 79, 80, 89, 90, 102, 103, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 118, 119, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 145, 146, 147, 148, 149, 156, 157, 158, 159, 167, 168, 169, 178, 179, 180, 189, 190, 192, 193, 194, 195, 196, 197, 203, 204, 205, 206, 207, 208, 213, 214, 215, 216, 217, 218, 223, 224, 225, 226, 227, 228, 234, 235, 236, 237, 238, 245, 246, 247, 248, 256, 257, 258, 260, 267, 268, 269, 270, 278, 279, 280, 283, 284, 285, 289, 290, 293, 294, 295, 304, 305, 306, 307, 314, 315, 316, 317, 324, 325, 326, 327, 334, 335, 336, 337, 338, 339, 340, 345, 346, 347, 348, 349, 350, 356, 357, 358, 359, 360, 367, 368, 369, 370, 378, 379, 380, 389, 390, 405, 406, 407, 408, 409, 415, 416, 417, 418, 419, 425, 426, 427, 428, 429, 435, 436, 437, 438, 439, 445, 446, 447, 448, 449, 450, 456, 457, 458, 459, 460, 467, 468, 469, 470, 478, 479, 480, 489, 490, 506, 507, 508, 509, 516, 517, 518, 519, 526, 527, 528, 529, 536, 537, 538, 539, 540, 546, 547, 548, 549, 550, 556, 557, 558, 559, 560, 567, 568, 569, 570, 578, 579, 580, 589, 590, 607, 608, 609, 617, 618, 619, 627, 628, 629, 630, 637, 638, 639, 640, 647, 648, 649, 650, 657, 658, 659, 660, 667, 668, 669, 670, 678, 679, 680, 689, 690, 708, 709, 718, 719, 720, 728, 729, 730, 738, 739, 740, 748, 749, 750, 758, 759, 760, 768, 769, 770, 778, 779, 780, 789, 790, 809, 810, 819, 820, 829, 830, 839, 840, 849, 850, 859, 860, 869, 870, 879, 880, 889, 890, 919, 932, 942, 943, 952, 953, 962, 963, 971, 972, 973, 981, 982, 983, 991, 992, 993, 1002, 1003, 1012, 1013, 1014, 1023, 1024, 1025, 1026, 1034, 1035, 1036, 1037, 1038, 1045, 1046, 1047, 1048, 1056, 1057, 1058, 1062, 1067, 1068, 1072, 1078, 1082, 1083, 1084, 1085, 1092, 1093, 1094, 1095, 1096, 1097, 1102, 1103, 1104, 1105, 1106, 1107, 1112, 1113, 1114, 1115, 1116, 1117, 1123, 1124, 1125, 1126, 1127, 1128, 1134, 1135, 1136, 1137, 1138, 1145, 1146, 1147, 1148, 1156, 1157, 1158, 1167, 1168, 1178, 1179, 1182, 1183, 1184, 1185, 1186, 1189, 1192, 1193, 1194, 1195, 1196, 1197, 1203, 1204, 1205, 1206, 1207, 1213, 1214, 1215, 1216, 1217, 1223, 1224, 1225, 1226, 1227, 1234, 1235, 1236, 1237, 1245, 1246, 1247, 1248, 1256, 1257, 1258, 1259, 1267, 1268, 1269, 1273, 1278, 1279, 1283, 1284, 1289, 1293, 1294, 1295, 1296, 1304, 1305, 1306, 1307, 1314, 1315, 1316, 1317, 1318, 1324, 1325, 1326, 1327, 1328, 1334, 1335, 1336, 1337, 1338, 1339, 1345, 1346, 1347, 1348, 1349, 1356, 1357, 1358, 1359, 1367, 1368, 1369, 1378, 1379, 1389, 1394, 1395, 1396, 1397, 1398, 1405, 1406, 1407, 1408, 1415, 1416, 1417, 1418, 1425, 1426, 1427, 1428, 1435, 1436, 1437, 1438, 1445, 1446, 1447, 1448, 1449, 1456, 1457, 1458, 1459, 1467, 1468, 1469, 1470, 1478, 1479, 1480, 1489, 1490, 1495, 1496, 1506, 1507, 1508, 1516, 1517, 1518, 1526, 1527, 1528, 1529, 1530, 1536, 1537, 1538, 1539, 1540, 1546, 1547, 1548, 1549, 1550, 1556, 1557, 1558, 1559, 1560, 1567, 1568, 1569, 1570, 1578, 1579, 1580, 1589, 1590, 1607, 1608, 1609, 1617, 1618, 1619, 1627, 1628, 1629, 1630, 1637, 1638, 1639, 1640, 1647, 1648, 1649, 1650, 1657, 1658, 1659, 1660, 1667, 1668, 1669, 1670, 1678, 1679, 1680, 1689, 1690, 1708, 1709, 1718, 1719, 1720, 1728, 1729, 1730, 1738, 1739, 1740, 1748, 1749, 1750, 1758, 1759, 1760, 1768, 1769, 1770, 1778, 1779, 1780, 1789, 1790, 1809, 1810, 1819, 1820, 1829, 1830, 1839, 1840, 1849, 1850, 1859, 1860, 1862, 1869, 1870, 1872, 1879, 1880, 1882, 1889, 1890, 1892, 1902, 1910, 1912, 1920, 1930, 1932, 1940, 1942, 1950, 1952, 1960, 1962, 1963, 1970, 1972, 1973, 1974, 1980, 1982, 1983, 1984, 1990, 1992, 1993, 1994, 2003, 2004, 2013, 2014, 2015, 2023, 2024, 2025, 2034, 2035, 2045, 2046, 2053, 2056, 2057, 2063, 2064, 2067, 2073, 2074, 2083, 2084, 2085, 2093, 2094, 2095, 2096, 2097, 2103, 2104, 2105, 2106, 2107, 2113, 2114, 2115, 2116, 2117, 2123, 2124, 2125, 2126, 2127, 2128, 2134, 2135, 2136, 2137, 2138, 2145, 2146, 2147, 2148, 2156, 2157, 2158, 2167, 2168, 2178, 2183, 2184, 2185, 2186, 2187, 2193, 2194, 2195, 2196, 2197, 2203, 2204, 2205, 2206, 2207, 2213, 2214, 2215, 2216, 2217, 2223, 2224, 2225, 2226, 2227, 2234, 2235, 2236, 2237, 2238, 2245, 2246, 2247, 2248, 2256, 2257, 2258, 2267, 2268, 2278, 2283, 2284, 2285, 2286, 2287, 2293, 2294, 2295, 2296, 2297, 2304, 2305, 2306, 2307, 2314, 2315, 2316, 2317, 2324, 2325, 2326, 2327, 2334, 2335, 2336, 2337, 2338, 2345, 2346, 2347, 2348, 2356, 2357, 2358, 2359, 2367, 2368, 2369, 2378, 2379, 2384, 2389, 2394, 2395, 2396, 2397, 2405, 2406, 2407, 2408, 2415, 2416, 2417, 2418, 2425, 2426, 2427, 2428, 2435, 2436, 2437, 2438, 2439, 2445, 2446, 2447, 2448, 2449, 2456, 2457, 2458, 2459, 2467, 2468, 2469, 2478, 2479, 2480, 2489, 2490, 2495, 2496, 2497, 2506, 2507, 2508, 2516, 2517, 2518, 2526, 2527, 2528, 2530, 2536, 2537, 2538, 2539, 2540, 2546, 2547, 2548, 2549, 2550, 2556, 2557, 2558, 2559, 2560, 2567, 2568, 2569, 2570, 2578, 2579, 2580, 2589, 2590, 2607, 2608, 2609, 2617, 2618, 2619, 2627, 2628, 2629, 2630, 2637, 2638, 2639, 2640, 2647, 2648, 2649, 2650, 2657, 2658, 2659, 2660, 2667, 2668, 2669, 2670, 2678, 2679, 2680, 2689, 2690, 2708, 2709, 2718, 2719, 2720, 2728, 2729, 2730, 2738, 2739, 2740, 2748, 2749, 2750, 2758, 2759, 2760, 2768, 2769, 2770, 2778, 2779, 2780, 2789, 2790, 2809, 2810, 2819, 2820, 2829, 2830, 2839, 2840, 2849, 2850, 2859, 2860, 2869, 2870, 2879, 2880, 2889, 2890, 2903, 2910, 2913, 2920, 2923, 2930, 2940, 2943, 2950, 2953, 2960, 2963, 2970, 2973, 2980, 2983, 2984, 2990, 2993, 2994, 3004, 3005, 3014, 3015, 3024, 3025, 3026, 3027, 3034, 3035, 3036, 3037, 3038, 3045, 3046, 3047, 3048, 3056, 3057, 3058, 3067, 3068, 3078, 3084, 3085, 3086, 3087, 3094, 3095, 3096, 3097, 3104, 3105, 3106, 3107, 3114, 3115, 3116, 3117, 3124, 3125, 3126, 3127, 3128, 3134, 3135, 3136, 3137, 3138, 3145, 3146, 3147, 3148, 3156, 3157, 3158, 3167, 3168, 3178, 3179, 3184, 3185, 3186, 3189, 3194, 3195, 3196, 3197, 3204, 3205, 3206, 3207, 3214, 3215, 3216, 3217, 3224, 3225, 3226, 3227, 3228, 3234, 3235, 3236, 3237, 3238, 3239, 3245, 3246, 3247, 3248, 3249, 3256, 3257, 3258, 3259, 3267, 3268, 3269, 3278, 3279, 3289, 3294, 3295, 3296, 3297, 3298, 3304, 3305, 3306, 3307, 3308, 3314, 3315, 3316, 3317, 3318, 3324, 3325, 3326, 3327, 3328, 3334, 3335, 3336, 3337, 3338, 3345, 3346, 3347, 3348, 3349, 3356, 3357, 3358, 3359, 3367, 3368, 3369, 3378, 3379, 3389, 3394, 3395, 3396, 3397, 3398, 3405, 3406, 3407, 3408, 3415, 3416, 3417, 3418, 3425, 3426, 3427, 3428, 3435, 3436, 3437, 3438, 3445, 3446, 3447, 3448, 3449, 3456, 3457, 3458, 3459, 3467, 3468, 3469, 3478, 3479, 3489, 3495, 3496, 3497, 3498, 3506, 3507, 3508, 3516, 3517, 3518, 3526, 3527, 3528, 3530, 3536, 3537, 3538, 3539, 3540, 3546, 3547, 3548, 3549, 3550, 3556, 3557, 3558, 3559, 3560, 3567, 3568, 3569, 3570, 3578, 3579, 3580, 3589, 3590, 3607, 3608, 3609, 3617, 3618, 3619, 3627, 3628, 3629, 3630, 3637, 3638, 3639, 3640, 3647, 3648, 3649, 3650, 3657, 3658, 3659, 3660, 3667, 3668, 3669, 3670, 3678, 3679, 3680, 3689, 3690, 3708, 3709, 3718, 3719, 3720, 3728, 3729, 3730, 3738, 3739, 3740, 3748, 3749, 3750, 3758, 3759, 3760, 3768, 3769, 3770, 3778, 3779, 3780, 3789, 3790, 3809, 3810, 3819, 3820, 3829, 3830, 3839, 3840, 3849, 3850, 3859, 3860, 3869, 3870, 3879, 3880, 3889, 3890, 3919, 3939, 3959, 3979, 3995, 4005, 4006, 4008, 4009, 4015, 4016, 4017, 4018, 4019, 4025, 4026, 4027, 4028, 4029, 4035, 4036, 4037, 4038, 4039, 4045, 4046, 4047, 4048, 4049, 4056, 4057, 4058, 4059, 4067, 4068, 4069, 4078, 4079, 4089, 4095, 4096, 4097, 4098, 4105, 4106, 4107, 4108, 4115, 4116, 4117, 4118, 4125, 4126, 4127, 4128, 4135, 4136, 4137, 4138, 4139, 4145, 4146, 4147, 4148, 4149, 4156, 4157, 4158, 4159, 4167, 4168, 4169, 4178, 4179, 4189, 4195, 4196, 4197, 4198, 4205, 4206, 4207, 4208, 4215, 4216, 4217, 4218, 4225, 4226, 4227, 4228, 4235, 4236, 4237, 4238, 4239, 4245, 4246, 4247, 4248, 4249, 4256, 4257, 4258, 4259, 4267, 4268, 4269, 4278, 4279, 4289, 4295, 4296, 4297, 4298, 4305, 4306, 4307, 4308, 4315, 4316, 4317, 4318, 4325, 4326, 4327, 4328, 4335, 4336, 4337, 4338, 4339, 4345, 4346, 4347, 4348, 4349, 4356, 4357, 4358, 4359, 4367, 4368, 4369, 4378, 4379, 4389, 4395, 4396, 4397, 4398, 4405, 4406, 4407, 4408, 4415, 4416, 4417, 4418, 4425, 4426, 4427, 4428, 4435, 4436, 4437, 4438, 4439, 4445, 4446, 4447, 4448, 4449, 4456, 4457, 4458, 4459, 4467, 4468, 4469, 4478, 4479, 4480, 4489, 4490, 4495, 4496, 4497, 4506, 4507, 4508, 4516, 4517, 4518, 4526, 4527, 4528, 4530, 4536, 4537, 4538, 4539, 4540, 4546, 4547, 4548, 4549, 4550, 4556, 4557, 4558, 4559, 4560, 4567, 4568, 4569, 4570, 4578, 4579, 4580, 4589, 4590, 4607, 4608, 4609, 4617, 4618, 4619, 4627, 4628, 4629, 4630, 4637, 4638, 4639, 4640, 4647, 4648, 4649, 4650, 4657, 4658, 4659, 4660, 4667, 4668, 4669, 4670, 4678, 4679, 4680, 4689, 4690, 4708, 4709, 4718, 4719, 4720, 4728, 4729, 4730, 4738, 4739, 4740, 4748, 4749, 4750, 4758, 4759, 4760, 4768, 4769, 4770, 4778, 4779, 4780, 4789, 4790, 4809, 4810, 4819, 4820, 4829, 4830, 4839, 4840, 4849, 4850, 4859, 4860, 4869, 4870, 4879, 4880, 4889, 4890, 4919, 4939, 4959, 4979, 4995, 5006, 5008, 5009, 5016, 5017, 5018, 5019, 5026, 5027, 5028, 5029, 5036, 5037, 5038, 5039, 5046, 5047, 5048, 5049, 5056, 5057, 5058, 5059, 5067, 5068, 5069, 5078, 5079, 5089, 5096, 5097, 5098, 5106, 5107, 5108, 5116, 5117, 5118, 5126, 5127, 5128, 5129, 5136, 5137, 5138, 5139, 5146, 5147, 5148, 5149, 5156, 5157, 5158, 5159, 5167, 5168, 5169, 5178, 5179, 5189, 5196, 5197, 5198, 5206, 5207, 5208, 5216, 5217, 5218, 5226, 5227, 5228, 5229, 5236, 5237, 5238, 5239, 5246, 5247, 5248, 5249, 5256, 5257, 5258, 5259, 5267, 5268, 5269, 5278, 5279, 5289, 5296, 5297, 5298, 5306, 5307, 5308, 5316, 5317, 5318, 5326, 5327, 5328, 5329, 5336, 5337, 5338, 5339, 5340, 5346, 5347, 5348, 5349, 5350, 5356, 5357, 5358, 5359, 5360, 5367, 5368, 5369, 5370, 5378, 5379, 5380, 5389, 5390, 5406, 5407, 5408, 5409, 5416, 5417, 5418, 5419, 5426, 5427, 5428, 5429, 5436, 5437, 5438, 5439, 5440, 5446, 5447, 5448, 5449, 5450, 5456, 5457, 5458, 5459, 5460, 5467, 5468, 5469, 5470, 5478, 5479, 5480, 5489, 5490, 5506, 5507, 5508, 5509, 5516, 5517, 5518, 5519, 5526, 5527, 5528, 5529, 5536, 5537, 5538, 5539, 5540, 5546, 5547, 5548, 5549, 5550, 5556, 5557, 5558, 5559, 5560, 5567, 5568, 5569, 5570, 5578, 5579, 5580, 5589, 5590, 5607, 5608, 5609, 5617, 5618, 5619, 5627, 5628, 5629, 5630, 5637, 5638, 5639, 5640, 5647, 5648, 5649, 5650, 5657, 5658, 5659, 5660, 5667, 5668, 5669, 5670, 5678, 5679, 5680, 5689, 5690, 5708, 5709, 5718, 5719, 5720, 5728, 5729, 5730, 5738, 5739, 5740, 5748, 5749, 5750, 5758, 5759, 5760, 5768, 5769, 5770, 5778, 5779, 5780, 5789, 5790, 5809, 5810, 5819, 5820, 5829, 5830, 5839, 5840, 5849, 5850, 5859, 5860, 5869, 5870, 5879, 5880, 5889, 5890, 5919, 5939, 5959, 5979, 6008, 6017, 6018, 6027, 6028, 6037, 6038, 6047, 6048, 6057, 6058, 6067, 6068, 6078, 6087, 6097, 6098, 6107, 6108, 6117, 6118, 6127, 6128, 6137, 6138, 6147, 6148, 6157, 6158, 6167, 6168, 6178, 6187, 6197, 6198, 6207, 6208, 6217, 6218, 6227, 6228, 6237, 6238, 6247, 6248, 6257, 6258, 6267, 6268, 6278, 6287, 6297, 6298, 6307, 6308, 6317, 6318, 6327, 6328, 6337, 6338, 6347, 6348, 6357, 6358, 6367, 6368, 6378, 6387, 6397, 6398, 6407, 6408, 6417, 6418, 6427, 6428, 6437, 6438, 6447, 6448, 6457, 6458, 6467, 6468, 6478, 6487, 6497, 6498, 6507, 6508, 6517, 6518, 6527, 6528, 6537, 6538, 6547, 6548, 6557, 6558, 6567, 6568, 6578, 6587, 6597, 6598, 6607, 6608, 6617, 6618, 6627, 6628, 6637, 6638, 6647, 6648, 6657, 6658, 6667, 6668, 6678, 6687, 6697, 6698, 6708, 6718, 6728, 6738, 6748, 6758, 6768, 6778, 7676, 7696, 7706, 7716, 7726, 7736, 7746, 7756, 8201, 8252, 8272, 8292, 8302, 8312, 8553, 8563, 8573, 8583, 8593, 8603, 8613, 8623, 8724, 8734, 8925, 8935, 8945 (last term of the sequence).

Final values for each digit:

0: 624

1: 822

2: 834

3: 864

4: 874

5: 894

6: 779

7: 697

8: 697

9: 617

Eric’s Format:

10             12      13      14      15      16      17      18      19

20                     23      24      25      26      27      28      29

30                             34      35      36      37      38      39

40                                     45      46      47      48      49

50                                             56      57      58      59

60                                                     67      68      69

70                                                             78      79

80                                                                     89

90

102     103     104     105     106     107     108     109

112     113     114     115     116     117     118     119

123     124     125     126     127     128     129

134     135     136     137     138     139

145     146     147     148     149

156     157     158     159

167     168     169

178     179

180                                                                    189

190            192     193     194     195     196     197

203     204     205     206     207     208

213     214     215     216     217     218

223     224     225     226     227     228

234     235     236     237     238

245     246     247     248

256     257     258

260                                                    267     268     269

270                                                            278     279

280                    283     284     285                             289

290                    293     294     295

304     305     306     307

314     315     316     317

324     325     326     327

334     335     336     337     338     339

340                                    345     346     347     348     349

350                                            356     357     358     359

360                                                    367     368     369

370                                                            378     379

380                                                                    389

390

405     406     407     408     409

415     416     417     418     419

425     426     427     428     429

435     436     437     438     439

445     446     447     448     449

450                                            456     457     458     459

460                                                    467     468     469

470                                                            478     479

480                                                                    489

490

506     507     508     509

516     517     518     519

526     527     528     529

536     537     538     539

540                                            546     547     548     549

550                                            556     557     558     559

560                                                    567     568     569

570                                                            578     579

580                                                                    589

590

607     608     609

617     618     619

627     628     629

630                                                    637     638     639

640                                                    647     648     649

650                                                    657     658     659

660                                                    667     668     669

670                                                            678     679

680                                                                    689

690

708     709

718     719

720                                                            728     729

730                                                            738     739

740                                                            748     749

750                                                            758     759

760                                                            768     769

770                                                            778     779

780                                                                    789

790

809

810                                                                    819

820                                                                    829

830                                                                    839

840                                                                    849

850                                                                    859

860                                                                    869

870                                                                    879

880                                                                    889

890

919

932

942     943

952     953

962     963

971     972     973

981     982     983

991     992     993

1002    1003

1012    1013    1014

1023    1024    1025    1026

1034    1035    1036    1037    1038

1045    1046    1047    1048

1056    1057    1058

1062                                    1067    1068

1072                                            1078

1082    1083    1084    1085

1092    1093    1094    1095    1096    1097

1102    1103    1104    1105    1106    1107

1112    1113    1114    1115    1116    1117

1123    1124    1125    1126    1127    1128

1134    1135    1136    1137    1138

1145    1146    1147    1148

1156    1157    1158

1167    1168

1178    1179

1182    1183    1184    1185    1186                    1189

1192    1193    1194    1195    1196    1197

1203    1204    1205    1206    1207

1213    1214    1215    1216    1217

1223    1224    1225    1226    1227

1234    1235    1236    1237

1245    1246    1247    1248

1256    1257    1258    1259

1267    1268    1269

1273                                    1278    1279

1283    1284                                    1289

1293    1294    1295    1296

1304    1305    1306    1307

1314    1315    1316    1317    1318

1324    1325    1326    1327    1328

1334    1335    1336    1337    1338    1339

1345    1346    1347    1348    1349

1356    1357    1358    1359

1367    1368    1369

1378    1379

1389

1394    1395    1396    1397    1398

1405    1406    1407    1408

1415    1416    1417    1418

1425    1426    1427    1428

1435    1436    1437    1438

1445    1446    1447    1448    1449

1456    1457    1458    1459

1467    1468    1469

1470                                                           1478    1479

1480                                                                   1489

1490                                   1495    1496

1506    1507    1508

1516    1517    1518

1526    1527    1528    1529

1530                                           1536    1537    1538    1539

1540                                           1546    1547    1548    1549

1550                                           1556    1557    1558    1559

1560                                                   1567    1568    1569

1570                                                           1578    1579

1580                                                                   1589

1590

1607    1608    1609

1617    1618    1619

1627    1628    1629

1630                                                   1637    1638    1639

1640                                                   1647    1648    1649

1650                                                   1657    1658    1659

1660                                                   1667    1668    1669

1670                                                           1678    1679

1680                                                                   1689

1690

1708    1709

1718    1719

1720                                                           1728    1729

1730                                                           1738    1739

1740                                                           1748    1749

1750                                                           1758    1759

1760                                                           1768    1769

1770                                                           1778    1779

1780                                                                   1789

1790

1809

1810                                                                   1819

1820                                                                   1829

1830                                                                   1839

1840                                                                   1849

1850                                                                   1859

1860           1862                                                    1869

1870           1872                                                    1879

1880           1882                                                    1889

1890           1892

1902

1910           1912

1920

1930           1932

1940           1942

1950           1952

1960           1962    1963

1970           1972    1973    1974

1980           1982    1983    1984

1990           1992    1993    1994

2003    2004

2013    2014    2015

2023    2024    2025

2034    2035

2045    2046

2053                    2056    2057

2063    2064                    2067

2073    2074

2083    2084    2085

2093    2094    2095    2096    2097

2103    2104    2105    2106    2107

2113    2114    2115    2116    2117

2123    2124    2125    2126    2127    2128

2134    2135    2136    2137    2138

2145    2146    2147    2148

2156    2157    2158

2167    2168

2178

2183    2184    2185    2186    2187

2193    2194    2195    2196    2197

2203    2204    2205    2206    2207

2213    2214    2215    2216    2217

2223    2224    2225    2226    2227

2234    2235    2236    2237    2238

2245    2246    2247    2248

2256    2257    2258

2267    2268

2278

2283    2284    2285    2286    2287

2293    2294    2295    2296    2297

2304    2305    2306    2307

2314    2315    2316    2317

2324    2325    2326    2327

2334    2335    2336    2337    2338

2345    2346    2347    2348

2356    2357    2358    2359

2367    2368    2369

2378    2379

2384                                    2389

2394    2395    2396    2397

2405    2406    2407    2408

2415    2416    2417    2418

2425    2426    2427    2428

2435    2436    2437    2438    2439

2445    2446    2447    2448    2449

2456    2457    2458    2459

2467    2468    2469

2478    2479

2480                                                                   2489

2490                                   2495    2496    2497

2506    2507    2508

2516    2517    2518

2526    2527    2528

2530                                           2536    2537    2538    2539

2540                                           2546    2547    2548    2549

2550                                           2556    2557    2558    2559

2560                                                   2567    2568    2569

2570                                                           2578    2579

2580                                                                   2589

2590

2607    2608    2609

2617    2618    2619

2627    2628    2629

2630                                                   2637    2638    2639

2640                                                   2647    2648    2649

2650                                                   2657    2658    2659

2660                                                   2667    2668    2669

2670                                                           2678    2679

2680                                                                   2689

2690

2708    2709

2718    2719

2720                                                           2728    2729

2730                                                           2738    2739

2740                                                           2748    2749

2750                                                           2758    2759

2760                                                           2768    2769

2770                                                           2778    2779

2780                                                                   2789

2790

2809

2810                                                                   2819

2820                                                                   2829

2830                                                                   2839

2840                                                                   2849

2850                                                                   2859

2860                                                                   2869

2870                                                                   2879

2880                                                                   2889

2890

2903

2910                   2913

2920                   2923

2930

2940                   2943

2950                   2953

2960                   2963

2970                   2973

2980                   2983    2984

2990                   2993    2994

3004    3005

3014    3015

3024    3025    3026    3027

3034    3035    3036    3037    3038

3045    3046    3047    3048

3056    3057    3058

3067    3068

3078

3084    3085    3086    3087

3094    3095    3096    3097

3104    3105    3106    3107

3114    3115    3116    3117

3124    3125    3126    3127    3128

3134    3135    3136    3137    3138

3145    3146    3147    3148

3156    3157    3158

3167    3168

3178    3179

3184    3185    3186                    3189

3194    3195    3196    3197

3204    3205    3206    3207

3214    3215    3216    3217

3224    3225    3226    3227    3228

3234    3235    3236    3237    3238    3239

3245    3246    3247    3248    3249

3256    3257    3258    3259

3267    3268    3269

3278    3279

3289

3294    3295    3296    3297    3298

3304    3305    3306    3307    3308

3314    3315    3316    3317    3318

3324    3325    3326    3327    3328

3334    3335    3336    3337    3338

3345    3346    3347    3348    3349

3356    3357    3358    3359

3367    3368    3369

3378    3379

3389

3394    3395    3396    3397    3398

3405    3406    3407    3408

3415    3416    3417    3418

3425    3426    3427    3428

3435    3436    3437    3438

3445    3446    3447    3448    3449

3456    3457    3458    3459

3467    3468    3469

3478    3479

3489

3495    3496    3497    3498

3506    3507    3508

3516    3517    3518

3526    3527    3528

3530                                           3536    3537    3538    3539

3540                                           3546    3547    3548    3549

3550                                           3556    3557    3558    3559

3560                                                   3567    3568    3569

3570                                                           3578    3579

3580                                                                   3589

3590

3607    3608    3609

3617    3618    3619

3627    3628    3629

3630                                                   3637    3638    3639

3640                                                   3647    3648    3649

3650                                                   3657    3658    3659

3660                                                   3667    3668    3669

3670                                                           3678    3679

3680                                                                   3689

3690

3708    3709

3718    3719

3720                                                           3728    3729

3730                                                           3738    3739

3740                                                           3748    3749

3750                                                           3758    3759

3760                                                           3768    3769

3770                                                           3778    3779

3780                                                                   3789

3790

3809

3810                                                                   3819

3820                                                                   3829

3830                                                                   3839

3840                                                                   3849

3850                                                                   3859

3860                                                                   3869

3870                                                                   3879

3880                                                                   3889

3890

3919

3939

3959

3979

3995

4005    4006            4008    4009

4015    4016    4017    4018    4019

4025    4026    4027    4028    4029

4035    4036    4037    4038    4039

4045    4046    4047    4048    4049

4056    4057    4058    4059

4067    4068    4069

4078    4079

4089

4095    4096    4097    4098

4105    4106    4107    4108

4115    4116    4117    4118

4125    4126    4127    4128

4135    4136    4137    4138    4139

4145    4146    4147    4148    4149

4156    4157    4158    4159

4167    4168    4169

4178    4179

4189

4195    4196    4197    4198

4205    4206    4207    4208

4215    4216    4217    4218

4225    4226    4227    4228

4235    4236    4237    4238    4239

4245    4246    4247    4248    4249

4256    4257    4258    4259

4267    4268    4269

4278    4279

4289

4295    4296    4297    4298

4305    4306    4307    4308

4315    4316    4317    4318

4325    4326    4327    4328

4335    4336    4337    4338    4339

4345    4346    4347    4348    4349

4356    4357    4358    4359

4367    4368    4369

4378    4379

4389

4395    4396    4397    4398

4405    4406    4407    4408

4415    4416    4417    4418

4425    4426    4427    4428

4435    4436    4437    4438    4439

4445    4446    4447    4448    4449

4456    4457    4458    4459

4467    4468    4469

4478    4479

4480                                                                   4489

4490                                   4495    4496    4497

4506    4507    4508

4516    4517    4518

4526    4527    4528

4530                                           4536    4537    4538    4539

4540                                           4546    4547    4548    4549

4550                                           4556    4557    4558    4559

4560                                                   4567    4568    4569

4570                                                           4578    4579

4580                                                                   4589

4590

4607    4608    4609

4617    4618    4619

4627    4628    4629

4630                                                   4637    4638    4639

4640                                                   4647    4648    4649

4650                                                   4657    4658    4659

4660                                                   4667    4668    4669

4670                                                           4678    4679

4680                                                                   4689

4690

4708    4709

4718    4719

4720                                                           4728    4729

4730                                                           4738    4739

4740                                                           4748    4749

4750                                                           4758    4759

4760                                                           4768    4769

4770                                                           4778    4779

4780                                                                   4789

4790

4809

4810                                                                   4819

4820                                                                   4829

4830                                                                   4839

4840                                                                   4849

4850                                                                   4859

4860                                                                   4869

4870                                                                   4879

4880                                                                   4889

4890

4919

4939

4959

4979

4995

5006            5008    5009

5016    5017    5018    5019

5026    5027    5028    5029

5036    5037    5038    5039

5046    5047    5048    5049

5056    5057    5058    5059

5067    5068    5069

5078    5079

5089

5096    5097    5098

5106    5107    5108

5116    5117    5118

5126    5127    5128    5129

5136    5137    5138    5139

5146    5147    5148    5149

5156    5157    5158    5159

5167    5168    5169

5178    5179

5189

5196    5197    5198

5206    5207    5208

5216    5217    5218

5226    5227    5228    5229

5236    5237    5238    5239

5246    5247    5248    5249

5256    5257    5258    5259

5267    5268    5269

5278    5279

5289

5296    5297    5298

5306    5307    5308

5316    5317    5318

5326    5327    5328    5329

5336    5337    5338    5339

5340                                           5346    5347    5348    5349

5350                                           5356    5357    5358    5359

5360                                                   5367    5368    5369

5370                                                           5378    5379

5380                                                                   5389

5390

5406    5407    5408    5409

5416    5417    5418    5419

5426    5427    5428    5429

5436    5437    5438    5439

5440                                           5446    5447    5448    5449

5450                                           5456    5457    5458    5459

5460                                                   5467    5468    5469

5470                                                           5478    5479

5480                                                                   5489

5490

5506    5507    5508    5509

5516    5517    5518    5519

5526    5527    5528    5529

5536    5537    5538    5539

5540                                           5546    5547    5548    5549

5550                                           5556    5557    5558    5559

5560                                                   5567    5568    5569

5570                                                           5578    5579

5580                                                                   5589

5590

5607    5608    5609

5617    5618    5619

5627    5628    5629

5630                                                   5637    5638    5639

5640                                                   5647    5648    5649

5650                                                   5657    5658    5659

5660                                                   5667    5668    5669

5670                                                           5678    5679

5680                                                                   5689

5690

5708    5709

5718    5719

5720                                                           5728    5729

5730                                                           5738    5739

5740                                                           5748    5749

5750                                                           5758    5759

5760                                                           5768    5769

5770                                                           5778    5779

5780                                                                   5789

5790

5809

5810                                                                   5819

5820                                                                   5829

5830                                                                   5839

5840                                                                   5849

5850                                                                   5859

5860                                                                   5869

5870                                                                   5879

5880                                                                   5889

5890

5919

5939

5959

5979

6008

6017    6018

6027    6028

6037    6038

6047    6048

6057    6058

6067    6068

6078

6087

6097    6098

6107    6108

6117    6118

6127    6128

6137    6138

6147    6148

6157    6158

6167    6168

6178

6187

6197    6198

6207    6208

6217    6218

6227    6228

6237    6238

6247    6248

6257    6258

6267    6268

6278

6287

6297    6298

6307    6308

6317    6318

6327    6328

6337    6338

6347    6348

6357    6358

6367    6368

6378

6387

6397    6398

6407    6408

6417    6418

6427    6428

6437    6438

6447    6448

6457    6458

6467    6468

6478

6487

6497    6498

6507    6508

6517    6518

6527    6528

6537    6538

6547    6548

6557    6558

6567    6568

6578

6587

6597    6598

6607    6608

6617    6618

6627    6628

6637    6638

6647    6648

6657    6658

6667    6668

6678

6687

6697    6698

6708

6718

6728

6738

6748

6758

6768

6778

7676

7696

7706

7716

7726

7736

7746

7756

8201

8252

8272

8292

8302

8312

8553

8563

8573

8583

8593

8603

8613

8623

8724

8734

8925

8935

8945

Note from David Wilson :

At a(2024) = 8945, the largest digit count is 894 5's. There are no more elements up to 8950. At 8950 and beyond, the "count" part of the number exceeds 894, and so cannot be in the sequence. Ergo the sequence is finite, with largest element a(2024) = 8945.

__________

This sequence is now A102357

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