A permutation of N

(divide by the first new digit)

 

 

Hello SeqFans,

I guess this is a nice little permutation of the Naturals:

a(1)=1

a(n+1) is the smallest unused integer that starts with a digit dividing a(n).

 

S=1,10,2,11,12,3,13,14,7,15,5,16,4,17,18,9,19,100,20,101,102...

6 21 30...

Best,

.

 

____________

 

[Jim Nastos and Andrew Weimholt immediately corrected the typos above then came Alois Heinz]:

 

Dear Eric,

the first 10000 terms ...

Best, Alois.

 

S = 1, 10, 2, 11, 12, 3, 13, 14, 7, 15, 5, 16, 4, 17, 18, 6, 19, 100, 20, 21, 30, 22, 23, 101, 102, 24, 8, 25, 50, 26, 27, 9, 31, 103, 104, 28, 29, 105, 32, 40, 41, 106, 107, 108, 33, 34, 109, 110, 51, 35, 52, 42, 36, 37, 111, 38, 112, 43, 113, 114, 39, 115, 53, 116, 44, 45, 54, 60, 46, 117, 90, 55, 56, 47, 118, 119, 70, 57, 120, 48, 49, 71, 121, 122, 123, 124, 125, 58, 126, 61, 127, 128, 80, 59, 129, 130, 131, 132, 62, 133, 72, 63, 73, 134, 135, 91, 74, 136, 81, 92, 137, 138, 64, 82, 139, 140, 75, 141, 142, 143, 144, 65, 145, 146, 147, 76, 148, 149, 150, 66, 67, 151, 152, 83, 153, 93, 154, 77, 78, 68, 155, 156, 69, 157, 158, 159, 160, 84, 79, 161, 162, 94, 163, 164, 165, 166, 167, 168, 85, 169, 170, 171, 95, 172, 173, 174, 175, 176, 86, 177, 178, 179, 180, 96, 87, 181, 182, 183, 184, 88, 89, 185, 186, 187, 188, 189, 97, 190, 191, 192, 193, 194, 195, 196, 197, 198, 98, 199, 1000, 200, 201, 300, 202, 203, 700, 204, 205, 500, 206, 207, 99, 301, 701, 1001, 702, 208, 209, 1002, 210, 211, 1003, 1004, 212, 213, 302, 214, 215, 501, 303, 304, 216, 217, 703, 1005, 305, 502, 218, 219, 306, 220, 221, 1006, 222, 223, 1007, 1008, 224, 225, 307, 1009, 1010, 226, 227, 1011, 308, 228, 229, 1012, 230, 231, 309, 310, 232, 233, 1013, 1014, 234, 235, 503, 1015, 504, 236, 237, 311, 1016, 238, 239, 1017, 312, 240, 241, 1018, 242, 243, 313, 1019, 1020, 244, 245, 505, 506, 246, 247, 1021, 1022, 248, 249, 314, 250, 251, 1023, 315, 316, 252, 253, 1024, 254, 255, 317, 1025, 507, 318, 256, 257, 1026, 258, 259, 704, 260, 261, 319, 1027, 1028, 262, 263, 1029, 320, 264, 265, 508, 266, 267, 321, 322, 268, 269, 1030, 270, 271, 1031, 1032, 272, 273, 323, 1033, 1034, 274, 275, 509, 1035, 324, 276, 277, 1036, 278, 279, 325, 510, 280, 281, 1037, 1038, 282, 283, 1039, 1040, 284, 285, 326, 286, 287, 705, 327, 328, 288, 289, 1041, 329, 706, 290, 291, 330, 292, 293, 1042, 294, 295, 511, 707, 708, 296, 297, 331, 1043, 709, 1044, 298, 299, 1045, 512, 400, 401, 1046, 1047, 332, 402, 333, 334, 1048, 403, 1049, 1050, 335, 513, 336, 337, 1051, 1052, 404, 405, 338, 1053, 339, 340, 406, 710, 514, 1054, 1055, 515, 516, 341, 1056, 342, 343, 711, 344, 407, 1057, 712, 408, 345, 346, 1058, 1059, 347, 1060, 409, 1061, 1062, 348, 349, 1063, 1064, 410, 517, 1065, 350, 518, 713, 1066, 1067, 1068, 351, 352, 411, 353, 1069, 1070, 519, 354, 355, 520, 412, 413, 714, 356, 414, 357, 358, 1071, 359, 1072, 415, 521, 1073, 1074, 360, 361, 1075, 522, 362, 1076, 416, 417, 363, 364, 418, 1077, 365, 523, 1078, 715, 524, 419, 1079, 1080, 366, 367, 1081, 1082, 1083, 368, 420, 369, 370, 525, 371, 716, 421, 1084, 422, 1085, 526, 1086, 372, 373, 1087, 1088, 423, 374, 1089, 375, 376, 424, 425, 527, 1090, 528, 377, 1091, 1092, 378, 379, 1093, 1094, 1095, 380, 426, 381, 382, 1096, 427, 717, 383, 1097, 1098, 384, 385, 529, 1099, 718, 1100, 428, 429, 386, 1101, 387, 388, 430, 530, 531, 389, 1102, 1103, 1104, 390, 391, 1105, 532, 431, 1106, 719, 1107, 392, 432, 393, 394, 1108, 433, 1109, 1110, 395, 533, 1111, 1112, 434, 720, 396, 397, 1113, 398, 1114, 1115, 534, 399, 721, 722, 1116, 435, 535, 536, 436, 437, 1117, 1118, 1119, 1120, 438, 600, 439, 1121, 1122, 601, 1123, 1124, 440, 441, 723, 1125, 537, 1126, 1127, 724, 442, 1128, 443, 1129, 1130, 538, 1131, 1132, 444, 445, 539, 725, 540, 446, 1133, 1134, 602, 726, 603, 900, 447, 1135, 541, 1136, 448, 449, 1137, 1138, 1139, 1140, 450, 542, 1141, 727, 1142, 1143, 901, 1144, 451, 1145, 543, 1146, 604, 452, 453, 1147, 1148, 454, 1149, 1150, 544, 455, 545, 546, 605, 547, 1151, 1152, 456, 457, 1153, 1154, 1155, 548, 458, 1156, 459, 902, 1157, 1158, 606, 607, 1159, 1160, 460, 461, 1161, 903, 728, 462, 608, 463, 1162, 729, 904, 464, 465, 549, 905, 550, 551, 1163, 1164, 466, 1165, 552, 467, 1166, 1167, 1168, 468, 469, 730, 553, 731, 1169, 732, 470, 554, 1170, 555, 556, 471, 1171, 1172, 472, 473, 1173, 1174, 1175, 557, 1176, 474, 609, 733, 1177, 1178, 1179, 906, 610, 558, 611, 1180, 475, 559, 1181, 1182, 612, 476, 477, 907, 1183, 734, 1184, 478, 1185, 560, 479, 1186, 1187, 1188, 480, 481, 1189, 1190, 561, 1191, 1192, 482, 1193, 1194, 613, 1195, 562, 1196, 483, 735, 563, 1197, 736, 484, 485, 564, 486, 614, 1198, 1199, 1200, 487, 1201, 1202, 1203, 1204, 488, 489, 1205, 565, 566, 1206, 615, 567, 737, 1207, 1208, 490, 568, 491, 1209, 1210, 569, 1211, 738, 616, 492, 493, 1212, 494, 1213, 1214, 1215, 570, 571, 1216, 495, 572, 496, 497, 739, 1217, 1218, 617, 1219, 1220, 498, 618, 619, 1221, 1222, 1223, 1224, 499, 1225, 573, 1226, 1227, 1228, 1229, 1230, 574, 740, 575, 576, 620, 577, 1231, 1232, 741, 1233, 908, 1234, 1235, 578, 1236, 621, 909, 910, 579, 1237, 1238, 1239, 742, 743, 1240, 580, 581, 744, 622, 1241, 1242, 623, 745, 582, 624, 625, 583, 1243, 1244, 1245, 584, 800, 585, 586, 1246, 746, 1247, 1248, 626, 1249, 1250, 587, 1251, 911, 1252, 1253, 747, 912, 627, 1254, 628, 1255, 588, 629, 1256, 801, 913, 1257, 1258, 1259, 1260, 589, 1261, 1262, 1263, 1264, 802, 1265, 590, 591, 1266, 630, 592, 803, 1267, 748, 1268, 1269, 914, 1270, 593, 1271, 1272, 631, 1273, 1274, 749, 750, 594, 632, 804, 633, 1275, 595, 596, 1276, 1277, 1278, 634, 1279, 1280, 597, 1281, 751, 1282, 1283, 1284, 635, 598, 1285, 599, 1286, 1287, 915, 1288, 752, 805, 753, 1289, 1290, 636, 637, 754, 1291, 1292, 1293, 1294, 1295, 755, 1296, 638, 1297, 1298, 1299, 1300, 1301, 1302, 639, 916, 1303, 1304, 806, 1305, 917, 756, 640, 807, 1306, 1307, 1308, 641, 1309, 757, 1310, 1311, 1312, 808, 809, 1313, 1314, 642, 643, 1315, 1316, 758, 1317, 1318, 1319, 1320, 644, 759, 1321, 1322, 1323, 760, 810, 645, 1324, 1325, 1326, 646, 1327, 1328, 811, 1329, 1330, 761, 1331, 1332, 647, 1333, 1334, 1335, 1336, 812, 762, 648, 649, 1337, 763, 764, 1338, 650, 1339, 1340, 1341, 918, 651, 765, 919, 1342, 1343, 1344, 652, 1345, 1346, 1347, 1348, 1349, 1350, 653, 1351, 766, 1352, 813, 1353, 1354, 1355, 1356, 654, 655, 1357, 1358, 767, 1359, 920, 814, 1360, 815, 1361, 1362, 656, 816, 657, 921, 1363, 1364, 1365, 768, 658, 769, 1366, 1367, 1368, 659, 1369, 1370, 1371, 1372, 770, 771, 1373, 1374, 660, 661, 1375, 1376, 817, 1377, 922, 1378, 1379, 772, 1380, 662, 1381, 1382, 1383, 1384, 818, 1385, 1386, 663, 1387, 1388, 1389, 1390, 1391, 1392, 664, 819, 773, 1393, 774, 665, 775, 1394, 1395, 923, 1396, 1397, 1398, 666, 667, 1399, 1400, 776, 820, 1401, 1402, 1403, 1404, 668, 1405, 1406, 1407, 777, 778, 1408, 821, 1409, 1410, 669, 1411, 1412, 1413, 924, 670, 1414, 779, 1415, 1416, 671, 1417, 1418, 1419, 1420, 1421, 780, 672, 673, 1422, 674, 1423, 1424, 822, 675, 925, 1425, 1426, 1427, 1428, 676, 1429, 1430, 1431, 926, 1432, 823, 1433, 1434, 677, 1435, 781, 1436, 1437, 1438, 1439, 1440, 678, 679, 782, 1441, 1442, 783, 927, 928, 824, 825, 1443, 1444, 1445, 1446, 680, 826, 784, 785, 1447, 1448, 827, 1449, 786, 681, 1450, 1451, 1452, 682, 1453, 1454, 1455, 1456, 787, 1457, 1458, 683, 1459, 1460, 1461, 1462, 1463, 788, 1464, 684, 685, 1465, 1466, 1467, 929, 1468, 1469, 1470, 686, 789, 1471, 1472, 828, 687, 1473, 1474, 1475, 1476, 688, 829, 1477, 790, 1478, 1479, 1480, 830, 1481, 1482, 689, 1483, 1484, 791, 792, 690, 691, 1485, 930, 692, 1486, 1487, 1488, 693, 793, 1489, 1490, 1491, 794, 1492, 1493, 1494, 694, 1495, 1496, 831, 1497, 1498, 795, 1499, 1500, 695, 1501, 1502, 1503, 931, 796, 1504, 832, 833, 797, 1505, 798, 696, 697, 1506, 698, 1507, 1508, 1509, 1510, 1511, 1512, 699, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 799, 1520, 834, 1521, 932, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 835, 1529, 1530, 933, 1531, 1532, 1533, 1534, 1535, 1536, 836, 1537, 1538, 1539, 934, 1540, 1541, 1542, 1543, 1544, 837, 935, 1545, 1546, 1547, 1548, 936, 838, 1549, 1550, 1551, 1552, 839, 1553, 1554, 1555, 1556, 1557, 937, 1558, 1559, 1560, 840, 841, 1561, 1562, 1563, 1564, 1565, 1566, 938, 1567, 1568, 842, 1569, 1570, 1571, 1572, 1573, 1574, 1575, 939, 1576, 843, 1577, 1578, 1579, 1580, 1581, 1582, 1583, 1584, 844, 1585, 1586, 1587, 1588, 1589, 1590, 1591, 1592, 845, 1593, 940, 1594, 1595, 1596, 1597, 1598, 1599, 1600, 846, 941, 1601, 1602, 942, 1603, 1604, 1605, 1606, 1607, 1608, 847, 1609, 1610, 1611, 943, 1612, 1613, 1614, 1615, 1616, 848, 849, 1617, 1618, 1619, 1620, 944, 850, 1621, 1622, 1623, 1624, 851, 1625, 1626, 1627, 1628, 1629, 945, 946, 1630, 1631, 1632, 852, 1633, 1634, 1635, 1636, 1637, 1638, 947, 1639, 1640, 853, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 948, 1648, 854, 1649, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 855, 949, 1657, 1658, 1659, 1660, 1661, 1662, 1663, 1664, 856, 857, 1665, 950, 1666, 1667, 1668, 1669, 1670, 1671, 1672, 858, 1673, 1674, 951, 1675, 1676, 1677, 1678, 1679, 1680, 859, 1681, 1682, 1683, 952, 860, 1684, 1685, 1686, 1687, 1688, 861, 1689, 1690, 1691, 1692, 953, 1693, 1694, 1695, 1696, 862, 1697, 1698, 1699, 1700, 1701, 954, 955, 1702, 1703, 1704, 863, 1705, 1706, 1707, 1708, 1709, 1710, 956, 1711, 1712, 864, 865, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 957, 1720, 866, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 867, 1729, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 868, 1737, 958, 1738, 1739, 1740, 1741, 1742, 1743, 1744, 869, 1745, 1746, 959, 1747, 1748, 1749, 1750, 1751, 1752, 870, 1753, 1754, 1755, 960, 871, 1756, 1757, 1758, 1759, 1760, 872, 873, 961, 1761, 1762, 1763, 1764, 962, 1765, 1766, 1767, 1768, 874, 1769, 1770, 1771, 1772, 1773, 963, 964, 1774, 1775, 1776, 875, 1777, 1778, 1779, 1780, 1781, 1782, 965, 1783, 1784, 876, 1785, 1786, 1787, 1788, 1789, 1790, 1791, 966, 1792, 877, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 1800, 878, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 879, 1809, 967, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 880, 881, 1817, 1818, 968, 882, 969, 1819, 1820, 1821, 1822, 1823, 1824, 883, 1825, 1826, 1827, 970, 1828, 1829, 1830, 1831, 1832, 884, 1833, 1834, 1835, 1836, 971, 1837, 1838, 1839, 1840, 885, 1841, 1842, 1843, 1844, 1845, 972, 973, 1846, 1847, 1848, 886, 1849, 1850, 1851, 1852, 1853, 1854, 974, 1855, 1856, 887, 1857, 1858, 1859, 1860, 1861, 1862, 1863, 975, 1864, 888, 889, 1865, 1866, 1867, 1868, 1869, 1870, 1871, 1872, 890, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 1880, 891, 976, 892, 1881, 977, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 893, 1889, 1890, 978, 1891, 1892, 1893, 1894, 1895, 1896, 894, 1897, 1898, 1899, 979, 1900, 1901, 1902, 1903, 1904, 895, 1905, 1906, 1907, 1908, 980, 1909, 1910, 1911, 1912, 896, 897, 1913, 1914, 1915, 1916, 1917, 981, 982, 1918, 1919, 1920, 898, 1921, 1922, 1923, 1924, 1925, 1926, 983, 1927, 1928, 899, 1929, 1930, 1931, 1932, 1933, 1934, 1935, 984, 1936, 1937, 1938, 1939, 1940, 1941, 1942, 1943, 1944, 985, 1945, 1946, 1947, 1948, 1949, 1950, 1951, 1952, 1953, 986, 1954, 1955, 1956, 1957, 1958, 1959, 1960, 1961, 1962, 987, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971, 988, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 989, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 990, 991, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 992, 1999, 10000, 2000, 2001, 3000, 2002, 2003, 10001, 10002, 2004, 2005, 5000, 2006, 2007, 993, 3001, 10003, 7000, 2008, 2009, 7001, 10004, 2010, 2011, 10005, 3002, 2012, 2013, 3003, 3004, 2014, 2015, 5001, 3005, 5002, 2016, 994, 2017, 10006, 2018, 2019, 3006, 995, 5003, 10007, 10008, 996, 2020, 2021, 10009, 10010, 2022, 2023, 7002, 997, 10011, 3007, 10012, 2024, 2025, 998, 2026, 2027, 10013, 10014, 2028, 2029, 10015, 5004, 999, 3008, 2030, 2031, 3009, 3010, 2032, 2033, 10016, 2034, 2035, 5005, 5006, 2036, 2037, 3011, 10017, 3012, 2038, 2039, 10018, 2040, 2041, 10019, 10020, 2042, 2043, 3013, 10021, 10022, 2044, 2045, 5007, 3014, 2046, 2047, 10023, 3015, 3016, 2048, 2049, 3017, 7003, 10024, 2050, 2051, 7004, 2052, 2053, 10025, 5008, 2054, 2055, 3018, 2056, 2057, 10026, 2058, 2059, 10027, 10028, 2060, 2061, 3019, 10029, 3020, 2062, 2063, 10030, 2064, 2065, 5009, 10031, 7005, 3021, 3022, 2066, 2067, 3023, 10032, 2068, 2069, 10033, 10034, 2070, 2071, 10035, 3024, 2072, 2073, 3025, 5010, 2074, 2075, 5011, 10036, 2076, 2077, 10037, 10038, 2078, 2079, 3026, 2080, 2081, 10039, 10040, 2082, 2083, 10041, 3027, 3028, 2084, 2085, 3029, 10042, 2086, 2087, 10043, 10044, 2088, 2089, 10045, 5012, 2090, 2091, 3030, 2092, 2093, 7006, 2094, 2095, 5013, 3031, 7007, 7008, 2096, 2097, 3032, 2098, 2099, 10046, 2100, 2101, 10047, 3033, 3034, 2102, 2103, 3035, 5014, 2104, 2105, 5015, 5016, 2106, 2107, 7009, 10048, 2108, 2109, 3036, 2110, 2111, 10049, 10050, 2112, 2113, 10051, 10052, 2114, 2115, 3037, 10053, 3038, 2116, 2117, 10054, 2118, 2119, 10055, 5017, 10056, 2120, 2121, 3039, 3040, 2122, 2123, 10057, 10058, 2124, 2125, 5018, 2126, 2127, 3041, 10059, 3042, 2128, 2129, 10060, 2130, 2131, 10061, 10062, 2132, 2133, 3043, 10063, 10064, 2134, 2135, 5019, 3044, 2136, 2137, 10065, 3045, 3046, 2138, 2139, 3047, 10066, 2140, 2141, 10067, 10068, 2142, 2143, 10069, 10070, 2144, 2145, 3048, 2146, 2147, 10071, 3049, 10072, 2148, 2149, 7010, 2150, 2151, 3050, 2152, 2153, 10073, 7011, 3051, 3052, 2154, 2155, 5020, 2156, 2157, 3053, 10074, 2158, 2159, 10075, 5021, 10076, 2160, 2161, 10077, 3054, 2162, 2163, 3055, 5022, 2164, 2165, 5023, 10078, 2166, 2167, 10079, 10080, 2168, 2169, 3056, 2170, 2171, 10081, 10082, 2172, 2173, 10083, 3057, 3058, 2174, 2175, 3059, 7012, 2176, 2177, 7013, 10084, 2178, 2179, 10085, 5024, 2180, 2181, 3060, 2182, 2183, 10086, 2184, 2185, 5025, 3061, 10087, 7014, 2186, 2187, 3062, 2188, 2189, 10088, 2190, 2191, 7015, 5026, 2192, 2193, 3063, 3064, 2194, 2195, 5027, 10089, 3065, 5028, 2196, 2197, 10090, 2198, 2199, 3066, 2200, 2201, 10091, 10092, 2202, 2203, 10093, 10094, 2204, 2205, 3067, 10095, 3068, 2206, 2207, 10096, 2208, 2209, 10097, 10098, 2210, 2211, 3069, 3070, 2212, 2213, 10099, 10100, 2214, 2215, 5029, 10101, 3071, 10102, 2216, 2217, 3072, 2218, 2219, 7016, 2220, 2221, 10103, 10104, 2222, 2223, 3073, 7017, 3074, 2224, 2225, 5030, 2226, 2227, 10105, 5031, 3075, 3076, 2228, 2229, 3077, 10106, 2230, 2231, 10107, 3078, 2232, 2233, 7018, 2234, 2235, 3079, 10108, 2236, 2237, 10109, 10110, 2238, 2239, 10111, 10112, 2240, 2241, 3080, 2242, 2243, 10113, 3081, 3082, 2244, 2245, 5032, 2246, 2247, 3083, 10114, 2248, 2249, 10115, 5033, 7019, 10116, 2250, 2251, 10117, 10118, 2252, 2253, 3084, 2254, 2255, 5034, 2256, 2257, 10119, 3085, 5035, 5036, 2258, 2259, 3086, 2260, 2261, 7020, 2262, 2263, 10120, 2264, 2265, 3087, 3088, 2266, 2267, 10121, 10122, 2268, 2269, 10123, 10124, 2270, 2271, 3089, 10125, 3090, 2272, 2273, 10126, 2274, 2275, 5037, 3091, 10127, 10128, 2276, 2277, 3092, 2278, 2279, 10129, 7021, 7022, 2280, 2281, 10130, 2282, 2283, 3093, 3094, 2284, 2285, 5038, 2286, 2287, 10131, 3095, 5039, 10132, 2288, 2289, 3096, 2290, 2291, 10133, 10134, 2292, 2293, 10135, 5040, 2294, 2295, 3097, 10136, 2296, 2297, 10137, 3098, 2298, 2299, 10138, 2300, 2301, 3099, 3100, 2302, 2303, 7023, 3101, 7024, 2304, 2305, 5041, 10139, 10140, 2306, 2307, 3102, 2308, 2309, 10141, 10142, 2310, 2311, 10143, 3103, 10144, 2312, 2313, 3104, 2314, 2315, 5042, 2316, 2317, 7025, 5043, 3105, 3106, 2318, 2319, 3107, 10145, 5044, 2320, 2321, 10146, 2322, 2323, 10147, 10148, 2324, 2325, 3108, 2326, 2327, 10149, 3109, 10150, 2328, 2329, 10151, 10152, 2330, 2331, 3110, 2332, 2333, 10153, 10154, 2334, 2335, 5045, 5046, 2336, 2337, 3111, 3112, 2338, 2339, 10155, 3113, 10156, 2340, 2341, 10157, 7026, 2342, 2343, 3114, 2344, 2345, 5047, 7027, 10158, 2346, 2347, 10159, 10160, 2348, 2349, 3115, 5048, 2350, 2351, 10161, 3116, 2352, 2353, 10162, 2354, 2355, 3117, 3118, 2356, 2357, 10163, 10164, 2358, 2359, 7028, 2360, 2361, 3119, 10165, 5049, 3120, 2362, 2363, 10166, 2364, 2365, 5050, 2366, 2367, 3121, 10167, 3122, 2368, 2369, 10168, 2370, 2371, 10169, 10170, 2372, 2373, 3123, 3124, 2374, 2375, 5051, 10171, 7029, 3125, 5052, 2376, 2377, 10172, 2378, 2379, 3126, 2380, 2381, 10173, 3127, 10174, 2382, 2383, 10175, 5053, 10176, 2384, 2385, 3128, 2386, 2387, 7030, 2388, 2389, 10177, 10178, 2390, 2391, 3129, 3130, 2392, 2393, 10179, 3131, 10180, 2394, 2395, 5054, 2396, 2397, 3132, 2398, 2399, 10181, 10182, 2400, 2401, 7031, 10183, 10184, 2402, 2403, 3133, 10185, 3134, 2404, 2405, 5055, 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12828, 6338, 12829, 12830, 5973, 12831, 7511, 7512, 6339, 12832, 8065, 5974, 12833, 12834, 6340, 5975, 5976, 6341, 12835, 5977, 12836, 12837, 12838, 7513, 12839, 12840, 5978, 7514, 12841, 12842, 12843, 9145, 5979, 12844, 12845, 5980, 5981, 12846, 6342, 6343, 12847, 12848, 8066, 12849, 12850, 5982, 6344, 8067, 12851, 12852, 6345, 5983, 12853, 12854, 12855, 5984, 8068, 12856, 8069, 12857, 12858, 6346, 12859, 7515, 5985, 5986, 12860, 5987, 12861, 9146, 12862, 12863, 12864, 6347, 12865, 5988, 6348, 6349, 7516, 12866, 7517, 12867, 12868, 12869, 12870, 5989, 12871, 12872, 8070, 5990, 5991, 12873, 7518, 6350, 5992, 7519, 12874, 12875, 5993, 12876, 6351, 12877, 12878, 12879, 9147, 12880, 5994, 6352, 8071, 7520, 5995, 5996, 12881, 12882, 6353, 12883, 12884, 12885, 5997, 12886, 12887, 7521, 12888, 6354, 6355, 5998, 12889, 12890, 5999, 7522, 12891, 12892, 12893, 12894, 6356, 7523, 12895, 12896, 8072, 8073, 9148,...

 

[Charles Greathouse]:

 

> Yes, this is a permutation of the positive integers. Suppose not, then there is some least number which does not occur (since no numbers are repeated by definition). The last of the numbers occurring before it appears by some number N, after which point no multiples of the first digit of the number can occur. But these multiples will occur with all digits 1-9 infinitely often, and so will eventually be picked up regardless of what initial digits the terms of the sequence after the first N have.

 

Charles Greathouse

Analyst/Programmer

Case Western Reserve University

 

__________

 

Many thanks to all contributors good job, nice graph!

Best,

.