Stymied by the beast

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The following described sequence is a somewhat fanciful extension of Éric Angelini's latest effort, Two identical digits. In my version, the products of adjacent terms must contain a single occurrence of the three digits "666". Furthermore, those products may not contain any additional sixes. The lexicographically earliest sequence of distinct positive terms starts:

1, 666, 10, 1666, 4, 1665, 40, 1667, 400, 4165, 16, 4163, 160, 4164, 1600, 4167, 64, 1041, 640, 1042, 373, 42, 1111, 15, 444, 150, 2444, 506, 361, 988, 675, 395, 422, 203, 1422, 469, 398, 268, 1368, 173, 385, 329, 154, 303, 55, 1211, 406, 211, 79, 654, 316, 1635, 579, 616, 1082, 191, 349, 234, 285, 269, 114, 585, 849, 903, 738, 257, 2166, 251, 166, 751, 355, 723, 142, 223, 299, 534, 312, 1047, 78, 47, 780, 470, 1078, 547, 195, 188, 461, 906, 961, 694, 96, 2778, 6, 111, 60, 611, 551, 121, 146, 621, 365, 484, 427, 156, 235, 539, 94, 39, 171, 390, 940, 922, 453, 1273, 288, 926, 18, 37, 180, 370, 991, 148, 45, 1037, 450, 1480, 518, 287, 929, 61, 306, 561, 101, 165, 1010, 264, 1351, 493, 338, 286, 233, 402, 733, 773, 345, 483, 138, 157, 552, 1407, 474, 109, 1896, 879, 292, 605, 573, 242, 73, 913, 730, 1242, 537, 869, 767, 598, 267, 624, 1068, 1186, 181, 186, 1181, 302, 383, 174, 159, 419, 214, 1246, 271, 2458, 556, 1198, 367, 198, 867, 769, 997, 669, 548, 1034, 49, 34, 196, 85, 549, 340, 490, 136, 1225, 544, 1226, 87, 318, 524, 757, 273, 244, 683, 449, 438, 207, 322, 353, 1237, 1024, 1627, 84, 793, 248, 1075, 62, 43, 155, 172, 562, 1542, 123, 2542, 262, 636, 435, 613, 882, 113, 59, 452, 590, 774, 559, 477, 58, 1149, 145, 1839, 294, 339, 1294, 515, 712, 936, 178, 206, 411, 892, 747, 278, 959, 374, 459, 363, 382, 541, 308, 671, 993, 1678, 588, 1133, 802, 532, 1441, 226, 118, 387, 689, 194, 756, 1940, 1189, 485, 1374, 558, 727, 243, 686, 431, 1547, 237, 218, 948, 545, 1223, 1003, 222, 3, 1222, 30, 2220, 300, 2221, 546, 122, 153, 305, 612, 1939, 1071, 249, 589, 283, 702, 95, 807, 38, 307, 152, 1557, 538, 57, 117, 570, 1169, 714, 169, 572, 641, 182, 163, 1182, 663, 553, 522, 53, 1257, 530, 1258, 177, 258, 677, 645, 708, 758, 927, 719, 51, 366, 510, 915, 204, 866, 77, 606, 44, 2197, 440, 3106, 261, 106, 629, 265, 1044, 638, 407, 1466, 201, 466, 143, 662, 643, 648, 1028, 843, 791, 126, 529, 315, 1291, 284, 446, 71, 1446, 571, 467, 798, 835, 499, 1837, 818, 337, 999, 334, 1499, 378, 388, 1718, 1487, 603, 608, 1261, 1060, 761, 219, 414, 161, 706, 1161, 574, 259, 296, 225, 1185, 436, 1528, 1863, 358, 27, 247, 270, 2467, 404, 66, 601, 610, 765, 871, 421, 346, 684, 536, 199, 737, 904, 295, 565, 472, 1137, 586, 455, 652, 1022, 212, 739, 902, 1483, 989, 394, 489, 1362, 372, 905, 593, 281, 344, 775, 86, 31, 215, 124, 457, 938, 711, 375, 1511, 441, 582, 252, 2209, 845, 789, 376, 975, 1094, 1432, 277, 858, 439, 653, 1021, 555, 12, 1389, 48, 1388, 480, 3471, 46, 471, 184, 362, 93, 717, 298, 1717, 33, 505, 330, 808, 1283, 1377, 397, 445, 824, 2022, 577, 658, 770, 865, 771, 246, 1271, 139, 1494, 473, 141, 26, 1141, 260, 1410, 1026, 65, 564, 526, 391, 2526, 891, 187, 918, 1053, 633, 911, 622, 403, 488, 1365, 884, 1727, 965, 691, 82, 313, 820, 1313, 1117, 597, 1116, 454, 779, 599, 734, 99, 673, 990, 1683, 102, 183, 255, 732, 91, 293, 876, 1035, 644, 647, 103, 356, 468, 698, 617, 886, 231, 202, 132, 2020, 533, 125, 1333, 2, 333, 20, 833, 8, 2083, 80, 3333, 5, 1332, 50, 3332, 200, 1833, 511, 424, 393, 1391, 479, 254, 656, 2540, 853, 781, 854, 379, 1073, 2242, 1234, 443, 462, 772, 1019, 193, 962, 1193, 475, 1403, 354, 129, 517, 98, 17, 392, 170, 980, 68, 245, 272, 2449, 634, 736, 2264, 692, 342, 423, 1316, 1654, 790, 1097, 945, 705, 52, 1281, 520, 1859, 974, 359, 1856, 1329, 923, 939, 497, 1341, 609, 602, 1107, 838, 107, 2492, 729, 503, 888, 75, 889, 750, 2222, 21, ...

The region from 740000 to 890000 is detailed here:

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