s20210622 Crashed Cycles: Basic parameters. Michael De Vlieger, St. Louis, Missouri, 202106251200. This data pertains to terms in the integer sequence s20210622. (See paper http://www.vincico.com/seq/s20210622.html.) A cycle c(i) in sequence a = s20210622 begins with the fruit of Condition 0 (i.e., novel m -> tau(m)), and the subsequent run of Condition 1 (i.e., extant m => (m + tau(u))). The first column renders index i of cycle c(i). Roman Numerals list the gorge number. When a gorge is interrupted with just one non-crashed cycle, we write A, B, etc. and render them as the same gorge number. The signature of a cycle is a(k) and a(k+1)-a(k), written joined by a "+" sign. Hence, the signature "4+32" begins with a(k) = 4, a(k+1) = 36. The k-ℓ designation lists the index of tau(m) and the run length of cycle c(i). For short cycles with ℓ <= 6, we list all terms. For longer cycles, we list the first 3 and the last 3 terms. The last term in a cycle is the cycle maximum M, which is novel in a. The prevailing low L(k+ℓ) is the hopper sequence number that must be exceeded by a term in the cycle so as not to have it crash. Cycle sig. k-ℓ a(k k+1 k+2 k+3 k+4 k+5 k+6) L(k+ℓ) -------------------------------------------------------------------------- I 84 12+12 910-4 12 24 30 38 46 60 II 102 8+12 1261-6 8 20 24 30 38 46 50 72 Cycle sig. k-ℓ a(k k+1 k+2 ... k+ℓ-2 k+ℓ-1 k+ℓ) L(k+ℓ) -------------------------------------------------------------------------- III 259 8+8 6920-40 8 16 20 . 215 217 221 222 IV 583 4+32 35478-24 4 36 39 . 187 191 195 840 584 8+2 35503-37 8 10 14 . 202 210 219 840 585 4+4 35541-58 4 8 11 . 336 344 359 840 586 2+6 35600-90 2 8 10 . 620 628 644 840 587 12+8 35691-97 12 20 26 . 646 650 656 840 588 10+24 35789-89 10 34 38 . 690 702 712 840 V 981 4+32 98340-25 4 36 39 . 191 195 197 1560 982 2+8 98366-89 2 10 12 . 488 492 501 1560 983 4+8 98456-86 4 12 15 . 598 604 612 1560 984 18+16 98543-81 18 34 40 . 622 628 636 1560 985 12+18 98625-96 12 30 36 . 638 642 648 1560 986 20+24 98722-113 20 44 50 . 974 980 1007 1560 VI-A 1132 4+32 130440-27 4 36 39 . 197 205 207 1848 1133 6+4 130468-40 6 10 14 . 221 223 227 1848 1134 2+4 130509-93 2 6 8 . 564 572 576 1848 1135 21+6 130603-96 21 27 31 . 602 614 635 1848 VI-B 1137 4+32 130924-36 4 36 39 . 231 233 241 1848 1138 2+2 130961-57 2 4 6 . 336 348 363 1848 1139 6+20 131019-70 6 26 30 . 564 576 580 1848 1140 12+6 131090-76 12 18 24 . 586 602 623 1848 1141 4+12 131167-143 4 16 19 . 1204 1216 1225 1848 1142 9+12 131311-155 9 21 24 . 1258 1272 1281 1848 1143 8+4 131467-191 8 12 16 . 1532 1544 1552 1848 1144 10+8 131659-188 10 18 22 . 1668 1698 1719 1848 Cycle sig. k-ℓ a(k k+1 k+2 ... k+ℓ-2 k+ℓ-1 k+ℓ) L(k+ℓ) -------------------------------------------------------------------------- VII 1163 4+32 136081-38 4 36 39 . 241 243 245 1890 1164 6+6 136120-84 6 12 16 . 492 501 509 1890 1165 2+12 136205-85 2 14 16 . 574 582 588 1890 1166 18+4 136291-84 18 22 28 . 606 614 632 1890 1167 8+8 136376-208 8 16 20 . 1808 1814 1841 1890 VIII 1171 4+32 137249-40 4 36 39 . 245 251 257 1890 1172 2+2 137290-68 2 4 6 . 412 424 439 1890 1173 2+6 137359-76 2 8 10 . 524 532 540 1890 1174 24+12 137436-81 24 36 44 . 542 548 556 1890 1175 6+12 137518-81 6 18 22 . 582 588 600 1890 1176 24+6 137600-82 24 30 38 . 678 686 704 1890 IX 1346 4+32 181994-41 4 36 39 . 251 257 259 2280 1347 4+2 182036-79 4 6 9 . 501 509 521 2280 1348 2+4 182116-96 2 6 8 . 550 556 568 2280 1349 8+6 182213-83 8 14 18 . 582 588 592 2280 1350 10+8 182297-90 10 18 22 . 656 662 680 2280 1351 16+24 182388-97 16 40 45 . 670 690 700 2280 1352 18+8 182486-175 18 26 32 . 1662 1686 1707 2280 1353 4+12 182662-192 4 16 19 . 1658 1664 1688 2280 1354 8+12 182855-221 8 20 24 . 2020 2028 2032 2280 1355 10+8 183077-238 10 18 22 . 2118 2122 2140 2280 Cycle sig. k-ℓ a(k k+1 k+2 ... k+ℓ-2 k+ℓ-1 k+ℓ) L(k+ℓ) -------------------------------------------------------------------------- X 1373 4+32 188010-43 4 36 39 . 259 261 265 2310 1374 4+6 188054-80 4 10 13 . 509 521 525 2310 1375 12+2 188135-70 12 14 20 . 530 532 544 2310 1376 12+12 188206-122 12 24 30 . 1082 1090 1101 2310 1377 4+20 188329-215 4 24 27 . 1996 2000 2012 2310 1378 6+4 188545-231 6 10 14 . 2024 2040 2060 2310 1379 12+8 188777-238 12 20 26 . 2052 2056 2064 2310 XI 1382 4+32 189550-44 4 36 39 . 261 265 271 2310 1383 2+4 189595-69 2 6 8 . 336 352 367 2310 1384 2+20 189665-67 2 22 24 . 420 432 447 2310 1385 4+6 189733-151 4 10 13 . 1348 1360 1385 2310 1386 4+32 189885-46 4 36 39 . 271 275 277 2310 1387 2+6 189932-56 2 8 10 . 334 340 355 2310 1388 4+4 189989-192 4 8 11 . 1662 1678 1708 2310 1389 12+6 190182-205 12 18 24 . 1884 1892 1904 2310 1390 20+12 190388-215 20 32 38 . 1926 1956 1964 2310 1391 6+16 190604-224 6 22 26 . 2066 2078 2084 2310 1392 6+8 190829-248 6 14 18 . 2158 2166 2172 2310 XII 1423 4+32 199767-47 4 36 39 . 275 277 283 2376 1424 2+2 199815-61 2 4 6 . 355 359 371 2376 1425 4+4 199877-84 4 8 11 . 584 588 596 2376 1426 6+12 199962-84 6 18 22 . 598 606 624 2376 1427 20+8 200047-89 20 28 34 . 700 712 724 2376 1428 6+4 200137-103 6 10 14 . 726 730 748 2376 1429 12+4 200241-115 12 16 22 . 726 734 740 2376 1430 12+6 200357-130 12 18 24 . 1102 1113 1119 2376 1431 4+12 200488-186 4 16 19 . 1636 1644 1648 2376 1432 10+32 200675-182 10 42 46 . 1648 1652 1673 2376 1433 4+12 200858-214 4 16 19 . 1908 1920 1928 2376 1434 8+24 201073-223 8 32 36 . 1904 1910 1916 2376 1435 6+12 201297-240 6 18 22 . 2166 2174 2184 2376 Cycle sig. k-ℓ a(k k+1 k+2 ... k+ℓ-2 k+ℓ-1 k+ℓ) L(k+ℓ) -------------------------------------------------------------------------- XIII 1657 4+32 273426-48 4 36 39 . 277 283 285 2970 1658 8+2 273475-77 8 10 14 . 521 525 527 2970 1659 4+2 273553-210 4 6 9 . 1890 1920 1932 2970 XIV 1740 32+40 302228-43 32 72 78 . 283 285 287 3120 1741 4+8 302272-143 4 12 15 . 1164 1174 1183 3120 1742 6+12 302416-230 6 18 22 . 2054 2072 2104 3120 1743 8+16 302647-284 8 24 28 . 2496 2500 2512 3120 1744 10+4 302932-283 10 14 18 . 2550 2554 2569 3120 1745 4+10 303216-328 4 14 17 . 2982 2994 3000 3120 XV-A 1880 4+32 354289-50 4 36 39 . 285 287 295 3432 1881 4+4 354340-82 4 8 11 . 525 527 529 3432 1882 3+12 354423-80 3 15 17 . 542 546 549 3432 1883 6+8 354504-90 6 14 18 . 644 656 672 3432 1884 24+6 354595-84 24 30 38 . 670 682 692 3432 1885 6+8 354680-172 6 14 18 . 1548 1554 1563 3432 1886 4+6 354853-265 4 10 13 . 2502 2506 2524 3432 1887 6+4 355119-290 6 10 14 . 2618 2622 2628 3432 1888 18+8 355410-321 18 26 32 . 2934 2946 2952 3432 XV-B 1890 4+32 356111-51 4 36 39 . 287 295 299 3432 1891 4+4 356163-83 4 8 11 . 527 529 541 3432 1892 2+4 356247-93 2 6 8 . 530 542 545 3432 1893 4+8 356341-86 4 12 15 . 618 630 651 3432 1894 8+10 356428-195 8 18 22 . 1626 1642 1663 3432 1895 2+8 356624-226 2 10 12 . 1844 1860 1887 3432 1896 8+6 356851-216 8 14 18 . 1906 1938 1952 3432 1897 12+24 357068-234 12 36 42 . 2054 2068 2080 3432 1898 24+6 357303-308 24 30 38 . 2852 2856 2864 3432 1899 10+8 357612-328 10 18 22 . 3000 3004 3008 3432 1900 14+4 357941-357 14 18 22 . 3258 3268 3272 3432 Cycle sig. k-ℓ a(k k+1 k+2 ... k+ℓ-2 k+ℓ-1 k+ℓ) L(k+ℓ) -------------------------------------------------------------------------- XVI 2116 4+32 449364-52 4 36 39 . 295 299 303 3990 2117 4+4 449417-93 4 8 11 . 596 608 629 3990 2118 4+6 449511-164 4 10 13 . 1316 1332 1357 3990 2119 4+8 449676-288 4 12 15 . 2512 2524 2532 3990 2120 12+15 449965-294 12 27 33 . 2542 2550 2560 3990 2121 20+4 450260-278 20 24 30 . 2544 2560 2572 3990 2122 6+8 450539-294 6 14 18 . 2666 2674 2680 3990 2123 16+4 450834-373 16 20 25 . 3448 3456 3460 3990 2124 12+4 451208-421 12 16 22 . 3916 3940 3952 3990 2125 20+24 451630-402 20 44 50 . 3862 3871 3887 3990 2126 6+18 452033-420 6 24 28 . 3916 3940 3948 3990 2127 24+16 452454-406 24 40 48 . 3914 3922 3928 3990 XVII 2146 32+30 461204-49 32 62 68 . 299 303 307 4050 2147 2+4 461254-104 2 6 8 . 629 635 647 4050 2148 2+4 461359-109 2 6 8 . 662 666 668 4050 2149 6+8 461469-96 6 14 18 . 678 690 696 4050 2150 16+8 461566-241 16 24 29 . 1994 2000 2016 4050 2151 36+8 461808-417 36 44 53 . 3928 3940 3949 4050 2152 4+12 462226-411 4 16 19 . 3916 3924 3936 4050 2153 24+4 462638-423 24 28 36 . 3994 4012 4020 4050 2154 24+24 463062-413 24 48 56 . 4014 4020 4028 4050 XVIII 2158 32+30 464776-50 32 62 68 . 303 307 311 4050 2159 2+2 464827-91 2 4 6 . 644 656 660 4050 2160 24+12 464919-239 24 36 44 . 2072 2104 2120 4050 2161 16+8 465159-324 16 24 29 . 2800 2820 2828 4050 2162 12+24 465484-317 12 36 42 . 2838 2868 2892 4050 Cycle sig. k-ℓ a(k k+1 k+2 ... k+ℓ-2 k+ℓ-1 k+ℓ) L(k+ℓ) -------------------------------------------------------------------------- XIX 2234 4+32 499839-55 4 36 39 . 307 311 313 4290 2235 2+2 499895-336 2 4 6 . 3054 3072 3076 4290 XX 2333 4+32 547444-56 4 36 39 . 311 313 315 4480 2334 12+2 547501-85 12 14 20 . 647 651 655 4480 2335 4+2 547587-239 4 6 9 . 2120 2128 2144 4480 2336 12+8 547827-347 12 20 26 . 3112 3128 3148 4480 2337 6+24 548175-340 6 30 34 . 3202 3208 3244 4480 2338 6+12 548516-355 6 18 22 . 3296 3300 3312 4480 2339 30+8 548872-353 30 38 46 . 3464 3468 3484 4480 2340 12+24 549226-378 12 36 42 . 3576 3584 3596 4480 2341 12+8 549605-444 12 20 26 . 4138 4150 4180 4480 XXI 2347 4+32 552523-57 4 36 39 . 313 315 317 4488 2348 2+12 552581-60 2 14 16 . 355 361 373 4488 2349 2+4 552642-71 2 6 8 . 362 374 377 4488 2350 4+4 552714-156 4 8 11 . 1328 1340 1365 4488 2351 16+8 552871-202 16 24 29 . 1674 1682 1692 4488 2352 18+12 553074-234 18 30 36 . 2024 2032 2036 4488 2353 6+12 553309-227 6 18 22 . 2030 2038 2044 4488 2354 12+20 553537-231 12 32 38 . 2074 2090 2100 4488 2355 36+6 553769-278 36 42 51 . 2560 2584 2600 4488 2356 24+16 554048-403 24 40 48 . 3860 3864 3888 4488 2357 30+4 554452-403 30 34 42 . 3888 3892 3900 4488 2358 36+16 554856-415 36 52 61 . 3924 3936 3968 4488 2359 16+4 555272-427 16 20 25 . 4102 4110 4128 4488 Cycle sig. k-ℓ a(k k+1 k+2 ... k+ℓ-2 k+ℓ-1 k+ℓ) L(k+ℓ) -------------------------------------------------------------------------- XXII-A 2704 4+32 742074-58 4 36 39 . 315 317 329 5320 2705 4+2 742133-68 4 6 9 . 424 439 445 5320 2706 4+8 742202-72 4 12 15 . 506 524 533 5320 2707 4+10 742275-89 4 14 17 . 608 620 641 5320 2708 2+8 742365-190 2 10 12 . 1648 1664 1672 5320 2709 16+16 742556-230 16 32 37 . 2002 2020 2035 5320 2710 8+24 742787-229 8 32 36 . 1988 1996 2004 5320 2711 12+4 743017-244 12 16 22 . 2026 2032 2048 5320 2712 12+12 743262-229 12 24 30 . 2094 2104 2112 5320 2713 28+4 743492-374 28 32 38 . 3504 3508 3516 5320 2714 12+16 743867-377 12 28 34 . 3638 3642 3648 5320 2715 28+8 744245-437 28 36 42 . 4178 4190 4220 5320 2716 12+4 744683-533 12 16 22 . 4938 4948 4956 5320 2717 24+32 745217-518 24 56 64 . 5070 5074 5080 5320 XXII-B 2719 4+32 746311-59 4 36 39 . 317 329 331 5320 2720 2+4 746371-78 2 6 8 . 429 445 457 5320 2721 2+8 746450-107 2 10 12 . 666 672 684 5320 2722 18+8 746558-136 18 26 32 . 1097 1101 1107 5320 2723 8+4 746695-181 8 12 16 . 1506 1522 1531 5320 2724 2+16 746877-206 2 18 20 . 1842 1866 1893 5320 2725 4+20 747084-265 4 24 27 . 2514 2532 2548 5320 2726 18+4 747350-283 18 22 28 . 2560 2572 2580 5320 2727 24+10 747634-284 24 34 42 . 2610 2618 2636 5320 2728 6+4 747919-292 6 10 14 . 2598 2606 2612 5320 2729 6+24 748212-292 6 30 34 . 2694 2718 2724 5320 2730 12+16 748505-291 12 28 34 . 2656 2660 2664 5320 2731 24+12 748797-352 24 36 44 . 3240 3244 3260 5320 2732 12+12 749150-360 12 24 30 . 3460 3468 3476 5320 2733 12+8 749511-368 12 20 26 . 3382 3398 3404 5320 2734 12+24 749880-380 12 36 42 . 3582 3614 3620 5320 2735 12+8 750261-381 12 20 26 . 3542 3560 3572 5320 2736 12+12 750643-408 12 24 30 . 3916 3936 3960 5320 2737 48+16 751052-415 48 64 74 . 4046 4082 4088 5320 2738 16+16 751468-522 16 32 37 . 5030 5040 5044 5320 Cycle sig. k-ℓ a(k k+1 k+2 ... k+ℓ-2 k+ℓ-1 k+ℓ) L(k+ℓ) -------------------------------------------------------------------------- XXIII 2869 4+32 828866-60 4 36 39 . 329 331 335 5610 2870 4+2 828927-70 4 6 9 . 445 457 465 5610 2871 8+4 828998-88 8 12 16 . 520 529 537 5610 2872 4+4 829087-82 4 8 11 . 546 558 561 5610 2873 8+8 829170-157 8 16 20 . 1340 1358 1383 5610 2874 4+32 829328-61 4 36 39 . 331 335 337 5610 2875 2+4 829390-80 2 6 8 . 457 465 469 5610 2876 4+2 829471-414 4 6 9 . 3924 3948 3972 5610 2877 12+24 829886-417 12 36 42 . 3924 3948 3956 5610 2878 12+12 830304-470 12 24 30 . 4724 4754 4760 5610 2879 32+12 830775-486 32 44 50 . 4782 4790 4796 5610 2880 12+16 831262-503 12 28 34 . 4906 4918 4928 5610 XXIV-A 2931 48+4 861280-59 48 52 62 . 335 337 341 5666 2932 4+2 861340-343 4 6 9 . 3148 3164 3185 5666 2933 12+6 861684-426 12 18 24 . 4078 4108 4112 5666 2934 10+16 862111-434 10 26 30 . 4154 4164 4172 5666 XXIV-B 2936 8+40 863163-61 8 48 52 . 337 341 343 5670 2937 4+4 863225-344 4 8 11 . 3164 3185 3191 5670 2938 2+12 863570-354 2 14 16 . 3260 3264 3276 5670 2939 36+6 863925-557 36 42 51 . 5610 5640 5652 5670 XXIV-C 2941 8+40 865069-62 8 48 52 . 341 343 347 5670 2942 2+4 865132-79 2 6 8 . 439 445 453 5670 2943 4+2 865212-90 4 6 9 . 616 624 640 5670 2944 16+8 865303-118 16 24 29 . 810 834 849 5670 2945 4+18 865422-197 4 22 25 . 1642 1663 1671 5670 2946 4+8 865620-226 4 12 15 . 2064 2068 2076 5670 2947 12+4 865847-296 12 16 22 . 2544 2560 2568 5670 2948 16+4 866144-342 16 20 25 . 3148 3164 3172 5670 2949 12+16 866487-340 12 28 34 . 3170 3174 3195 5670 2950 12+8 866828-358 12 20 26 . 3260 3272 3284 5670 2951 6+8 867187-355 6 14 18 . 3310 3314 3320 5670 2952 16+12 867543-354 16 28 33 . 3338 3344 3352 5670 2953 8+16 867898-418 8 24 28 . 3968 3976 4000 5670 2954 24+10 868317-411 24 34 42 . 4022 4046 4052 5670 2955 6+16 868729-432 6 22 26 . 4218 4230 4236 5670 2956 12+4 869162-529 12 16 22 . 4954 4970 4980 5670 Cycle sig. k-ℓ a(k k+1 k+2 ... k+ℓ-2 k+ℓ-1 k+ℓ) L(k+ℓ) -------------------------------------------------------------------------- XXV 2961 8+40 872005-63 8 48 52 . 343 347 351 5670 2962 8+2 872069-62 8 10 14 . 410 418 433 5670 2963 2+8 872132-101 2 10 12 . 630 636 652 5670 2964 6+4 872234-98 6 10 14 . 712 720 728 5670 2965 16+4 872333-101 16 20 25 . 706 722 736 5670 2966 12+4 872435-137 12 16 22 . 960 976 1003 5670 2967 4+20 872573-181 4 24 27 . 1712 1720 1741 5670 2968 2+6 872755-211 2 8 10 . 1828 1855 1861 5670 2969 2+12 872967-241 2 14 16 . 2108 2120 2136 5670 2970 16+24 873209-244 16 40 45 . 2138 2144 2180 5670 2971 12+4 873454-288 12 16 22 . 2490 2496 2528 5670 2972 12+10 873743-307 12 22 28 . 2862 2868 2888 5670 2973 12+8 874051-356 12 20 26 . 3164 3172 3188 5670 2974 6+8 874408-359 6 14 18 . 3314 3320 3336 5670 2975 16+8 874768-419 16 24 29 . 3900 3904 3920 5670 2976 30+20 875188-431 30 50 58 . 4278 4286 4316 5670 2977 12+12 875620-482 12 24 30 . 4704 4712 4736 5670 2978 16+8 876103-497 16 24 29 . 4724 4736 4748 5670 2979 6+16 876601-485 6 22 26 . 4770 4774 4780 5670 2980 12+16 877087-484 12 28 34 . 4728 4732 4768 5670 2981 12+36 877572-486 12 48 54 . 4782 4798 4816 5670 2982 20+8 878059-489 20 28 34 . 4778 4794 4812 5670 2983 12+12 878549-489 12 24 30 . 4822 4828 4844 5670 2984 12+16 879039-508 12 28 34 . 4954 4958 4968 5670 ...