| Radix Character Encoding | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V |
| W | X | Y | Z | a | b | c | d | e | f | g | h | i | j | k | l |
| Color Key | ||
|---|---|---|
| Orange | Fixed Point | number that becomes itself after one iteration |
| Green | Final Numbers | all numbers eventually reached, from all cycles |
| Purple | Cycle Start | iterations include entry into cycle, assuming it repeats |
| Red | Full Cycle | iterations include entire cycle, proving it repeats |
| Blue | Start Numbers | subset (optimization) of all numbers; minimal for full coverage |
| Gray | No Results | any calculation that has no results |
| Digits | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.97 step avg | 1.44 step avg | 8.35 step avg | 5.09 step avg | 10.88 step avg | 13.08 step avg | 8.40 step avg | 71.40 step avg | 14.58 step avg | 147.97 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 35× | 0s: 1s: 2s: 10× 350× 306× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 1× 377× 340× 678× 670× 658× 642× 622× 598× 570× 538× 502× 462× 418× 370× 318× 262× 202× 138× 70× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 1× 1,075× 2,136× 8,640× 34,560× 7,480× 6,673× 12,268× 2,934× 2,262× 4,222× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 1× 3,051× 3,946× 5,486× 12,226× 19,596× 32,882× 48,502× 58,694× 45,832× 67,576× 71,736× 58,934× 62,386× 54,414× 41,960× 32,356× 24,004× 11,298× 2,744× 314× 70× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 1× 106,441× 232,342× 263,946× 228,249× 255,226× 287,139× 321,082× 278,431× 246,301× 226,168× 184,069× 132,434× 124,868× 83,498× 80,050× 79,094× 73,365× 77,599× 67,581× 66,425× 81,192× 71,119× 82,320× 81,703× 88,787× 74,961× 73,278× 61,993× 71,207× 58,434× 50,565× 54,135× 55,963× 53,146× 34,059× 14,444× 14,936× 9,904× 15,290× 14,701× 10,970× 3,352× 5,620× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 1× 173,303× 449,180× 921,170× 1,426,980× 2,003,344× 2,279,922× 2,569,040× 3,219,574× 3,793,118× 3,564,542× 2,742,218× 1,941,494× 888,860× 547,684× 205,174× 164,446× 80,418× 6,720× 1,140× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 54s: 55s: 56s: 57s: 58s: 59s: 60s: 61s: 62s: 63s: 64s: 65s: 66s: 67s: 68s: 69s: 70s: 71s: 72s: 73s: 74s: 75s: 76s: 77s: 78s: 79s: 80s: 81s: 82s: 83s: 84s: 85s: 86s: 87s: 88s: 89s: 90s: 91s: 92s: 93s: 94s: 95s: 96s: 97s: 98s: 99s: 100s: 101s: 102s: 103s: 104s: 105s: 106s: 107s: 108s: 109s: 110s: 111s: 112s: 113s: 114s: 115s: 116s: 117s: 118s: 119s: 120s: 121s: 122s: 123s: 124s: 125s: 126s: 127s: 128s: 129s: 130s: 131s: 132s: 133s: 134s: 135s: 136s: 137s: 138s: 139s: 140s: 141s: 142s: 143s: 144s: 145s: 146s: 147s: 148s: 149s: 150s: 151s: 152s: 153s: 154s: 155s: 156s: 157s: 158s: 159s: 160s: 161s: 162s: 163s: 164s: 165s: 166s: 167s: 168s: 169s: 170s: 171s: 172s: 173s: 174s: 175s: 176s: 177s: 178s: 179s: 180s: 181s: 182s: 183s: 184s: 185s: 186s: 187s: 188s: 189s: 190s: 191s: 192s: 193s: 194s: 195s: 196s: 197s: 198s: 199s: 200s: 201s: 202s: 203s: 204s: 205s: 206s: 207s: 208s: 209s: 210s: 211s: 212s: 213s: 214s: 215s: 216s: 217s: 218s: 219s: 220s: 221s: 222s: 223s: 224s: 225s: 226s: 227s: 228s: 1× 297,719× 1,285,211× 1,463,922× 1,843,732× 1,776,875× 1,547,999× 1,470,207× 1,479,882× 1,586,731× 1,549,791× 1,517,267× 1,419,454× 1,169,529× 1,299,540× 1,106,141× 1,014,496× 998,801× 1,324,449× 1,511,053× 1,665,919× 1,835,676× 1,595,888× 1,605,210× 1,768,676× 1,612,807× 1,645,304× 1,499,717× 1,428,295× 1,741,358× 1,730,598× 1,720,272× 1,464,148× 1,136,570× 1,066,696× 1,122,142× 929,804× 648,136× 611,658× 823,848× 930,968× 913,920× 941,732× 665,297× 757,171× 760,646× 776,513× 751,854× 671,456× 901,968× 973,253× 1,032,077× 1,133,088× 1,056,661× 1,140,046× 1,084,958× 1,036,541× 1,074,806× 1,081,594× 974,035× 916,340× 975,844× 1,164,945× 1,118,616× 910,770× 820,376× 781,795× 806,278× 776,085× 798,571× 1,012,618× 950,513× 1,011,221× 917,956× 935,525× 786,695× 531,787× 673,233× 777,397× 720,840× 690,894× 832,159× 834,296× 818,842× 839,062× 819,111× 761,330× 799,844× 788,751× 789,721× 804,374× 810,792× 702,885× 724,880× 692,336× 466,480× 538,936× 644,170× 762,808× 795,828× 872,146× 1,021,765× 1,193,199× 997,703× 860,309× 901,970× 794,219× 635,195× 556,314× 359,265× 458,408× 542,058× 619,417× 566,687× 502,149× 530,037× 613,882× 583,947× 409,341× 437,267× 465,115× 316,511× 281,400× 278,442× 279,557× 239,240× 282,534× 283,432× 161,025× 106,289× 101,206× 141,696× 205,780× 165,651× 178,089× 225,185× 371,556× 403,447× 377,944× 411,350× 400,052× 338,831× 386,313× 480,425× 495,096× 562,394× 311,839× 306,483× 238,302× 266,301× 254,847× 321,925× 509,419× 472,020× 387,706× 558,344× 627,917× 690,494× 675,233× 694,344× 577,663× 444,455× 456,349× 315,594× 411,730× 395,763× 345,005× 324,458× 426,237× 527,157× 530,188× 512,570× 426,739× 356,794× 289,007× 412,173× 452,684× 313,798× 218,937× 324,113× 249,604× 258,372× 248,748× 233,183× 194,159× 103,830× 65,808× 27,937× 24,074× 31,434× 36,283× 48,900× 69,442× 74,552× 95,492× 94,704× 65,423× 53,696× 35,626× 31,488× 14,196× 22,208× 41,828× 33,511× 43,368× 40,942× 80,601× 66,129× 66,746× 107,909× 90,803× 136,184× 113,677× 149,221× 171,634× 198,904× 199,260× 217,045× 172,033× 123,623× 213,307× 145,290× 134,718× 126,951× 85,828× 70,813× 35,402× 11,455× 2,736× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 1× 547,889× 2,420,322× 5,954,094× 11,818,202× 22,793,260× 33,191,700× 38,293,976× 36,398,478× 30,354,118× 28,567,264× 34,993,958× 40,750,336× 36,971,620× 41,704,622× 43,615,514× 50,981,382× 41,722,672× 32,315,266× 21,638,604× 16,753,432× 17,857,178× 19,312,890× 24,139,868× 20,659,556× 16,522,500× 10,713,692× 7,063,690× 5,763,166× 2,778,030× 2,726,352× 1,267,008× 1,095,586× 898,980× 1,071,728× 1,649,602× 1,246,498× 1,277,802× 810,230× 289,442× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 54s: 55s: 56s: 57s: 58s: 59s: 60s: 61s: 62s: 63s: 64s: 65s: 66s: 67s: 68s: 69s: 70s: 71s: 72s: 73s: 74s: 75s: 76s: 77s: 78s: 79s: 80s: 81s: 82s: 83s: 84s: 85s: 86s: 87s: 88s: 89s: 90s: 91s: 92s: 93s: 94s: 95s: 96s: 97s: 98s: 99s: 100s: 101s: 102s: 103s: 104s: 105s: 106s: 107s: 108s: 109s: 110s: 111s: 112s: 113s: 114s: 115s: 116s: 117s: 118s: 119s: 120s: 121s: 122s: 123s: 124s: 125s: 126s: 127s: 128s: 129s: 130s: 131s: 132s: 133s: 134s: 135s: 136s: 137s: 138s: 139s: 140s: 141s: 142s: 143s: 144s: 145s: 146s: 147s: 148s: 149s: 150s: 151s: 152s: 153s: 154s: 155s: 156s: 157s: 158s: 159s: 160s: 161s: 162s: 163s: 164s: 165s: 166s: 167s: 168s: 169s: 170s: 171s: 172s: 173s: 174s: 175s: 176s: 177s: 178s: 179s: 180s: 181s: 182s: 183s: 184s: 185s: 186s: 187s: 188s: 189s: 190s: 191s: 192s: 193s: 194s: 195s: 196s: 197s: 198s: 199s: 200s: 201s: 202s: 203s: 204s: 205s: 206s: 207s: 208s: 209s: 210s: 211s: 212s: 213s: 214s: 215s: 216s: 217s: 218s: 219s: 220s: 221s: 222s: 223s: 224s: 225s: 226s: 227s: 228s: 229s: 230s: 231s: 232s: 233s: 234s: 235s: 236s: 237s: 238s: 239s: 240s: 241s: 242s: 243s: 244s: 245s: 246s: 247s: 248s: 249s: 250s: 251s: 252s: 253s: 254s: 255s: 256s: 257s: 258s: 259s: 260s: 261s: 262s: 263s: 264s: 265s: 266s: 267s: 268s: 269s: 270s: 271s: 272s: 273s: 274s: 275s: 276s: 277s: 278s: 279s: 280s: 281s: 282s: 283s: 284s: 285s: 286s: 287s: 288s: 289s: 290s: 291s: 292s: 293s: 294s: 295s: 296s: 297s: 298s: 299s: 300s: 301s: 302s: 303s: 304s: 305s: 306s: 307s: 308s: 309s: 310s: 311s: 312s: 313s: 314s: 315s: 316s: 317s: 318s: 319s: 320s: 321s: 322s: 323s: 324s: 325s: 326s: 327s: 328s: 329s: 330s: 331s: 332s: 333s: 334s: 335s: 336s: 337s: 338s: 339s: 340s: 341s: 342s: 343s: 344s: 345s: 346s: 347s: 348s: 349s: 350s: 351s: 352s: 353s: 354s: 355s: 356s: 357s: 358s: 359s: 360s: 361s: 1× 1,338,823× 11,907,298× 16,612,024× 17,809,795× 18,051,915× 19,384,066× 18,449,071× 17,798,401× 16,551,629× 20,091,861× 19,656,383× 19,100,110× 16,385,680× 17,502,567× 18,943,084× 22,541,980× 19,857,463× 19,425,597× 17,146,942× 16,288,354× 14,051,413× 15,005,564× 15,239,700× 15,744,311× 15,672,687× 16,082,738× 15,878,962× 13,756,388× 13,780,043× 16,113,010× 17,961,783× 18,269,328× 15,797,223× 17,036,310× 14,888,106× 15,896,058× 16,553,734× 14,359,378× 13,475,207× 10,664,525× 11,046,669× 12,291,320× 10,748,653× 9,365,919× 8,636,246× 9,167,364× 10,378,311× 9,121,276× 8,818,477× 9,585,601× 9,353,104× 9,240,724× 10,823,995× 7,599,043× 7,971,829× 8,245,000× 8,376,525× 8,335,583× 7,826,135× 6,095,247× 5,388,069× 7,401,332× 7,827,470× 8,808,838× 8,914,137× 9,890,419× 8,857,502× 8,621,681× 8,023,662× 8,421,072× 9,364,777× 10,000,020× 8,784,344× 7,198,472× 8,503,970× 8,562,667× 7,199,120× 6,608,732× 7,988,517× 9,114,765× 8,556,889× 7,294,685× 5,632,157× 6,697,934× 7,465,307× 7,395,996× 5,912,227× 6,377,787× 6,067,421× 7,836,005× 9,196,507× 7,138,609× 6,453,478× 4,663,043× 4,487,752× 5,567,162× 6,060,694× 6,528,302× 7,033,125× 6,163,914× 5,443,736× 3,810,520× 4,558,521× 6,089,726× 5,996,068× 5,925,282× 5,430,692× 5,239,697× 5,736,470× 7,790,640× 7,581,921× 8,645,824× 9,428,122× 11,359,901× 10,686,315× 10,156,507× 9,722,219× 8,632,717× 8,530,118× 8,181,921× 7,653,313× 7,760,265× 8,159,932× 7,408,193× 6,306,190× 6,136,052× 7,126,933× 5,832,479× 5,148,107× 4,863,379× 6,358,818× 7,536,625× 6,940,380× 8,276,764× 8,429,660× 8,153,892× 7,705,123× 9,225,663× 9,522,060× 11,642,824× 12,342,073× 13,375,647× 13,137,603× 10,533,220× 10,709,419× 11,687,479× 8,465,832× 6,588,793× 6,928,566× 7,931,237× 9,262,346× 10,508,001× 9,027,447× 8,223,664× 6,516,972× 6,507,769× 6,363,724× 6,469,424× 7,399,401× 8,663,745× 9,132,656× 10,012,425× 11,473,723× 8,942,328× 8,914,107× 7,141,883× 5,483,802× 5,928,208× 8,337,317× 8,553,502× 8,091,004× 7,861,086× 10,169,951× 8,532,057× 8,547,668× 10,069,414× 10,897,179× 10,882,652× 9,382,649× 10,123,863× 9,332,845× 8,013,530× 8,156,350× 8,906,090× 9,044,348× 8,358,287× 6,075,749× 5,547,349× 6,242,509× 6,799,084× 7,752,473× 6,337,759× 8,683,902× 7,430,329× 5,832,756× 6,936,628× 5,755,044× 6,829,902× 8,737,738× 11,020,300× 12,963,223× 13,311,459× 12,219,326× 11,921,542× 15,075,564× 18,900,485× 19,361,475× 18,268,113× 18,109,049× 16,058,879× 18,770,317× 21,164,418× 23,720,426× 24,917,185× 21,993,136× 20,374,654× 18,994,564× 18,122,836× 17,908,174× 18,674,442× 16,408,467× 17,397,140× 18,522,126× 18,762,196× 19,000,159× 18,174,337× 18,053,715× 19,665,969× 17,597,925× 20,560,575× 21,380,781× 19,785,130× 19,369,634× 18,665,243× 15,682,671× 13,265,426× 10,574,380× 11,651,907× 12,872,528× 15,329,581× 15,803,527× 14,340,317× 15,720,114× 16,405,329× 17,294,194× 15,517,558× 13,877,943× 12,042,220× 12,235,816× 11,676,600× 12,989,317× 11,294,544× 11,391,893× 8,845,340× 9,409,447× 9,861,933× 10,843,910× 8,710,830× 8,382,078× 8,724,908× 8,666,059× 6,975,024× 6,784,333× 6,908,321× 6,800,872× 6,522,046× 5,833,554× 5,389,274× 4,525,832× 3,922,419× 3,163,729× 3,118,836× 2,568,397× 3,476,329× 4,118,674× 4,529,675× 5,844,172× 6,938,372× 6,846,751× 5,078,955× 4,267,179× 5,523,184× 4,530,766× 3,528,817× 3,758,288× 2,743,798× 3,318,053× 3,502,510× 4,909,444× 3,948,583× 3,181,845× 3,665,127× 3,659,276× 4,532,542× 4,074,864× 4,688,942× 4,284,383× 4,065,712× 3,515,875× 3,073,679× 3,396,530× 3,533,985× 4,209,462× 4,136,533× 4,780,523× 5,592,128× 4,858,255× 6,395,281× 8,013,342× 5,643,211× 4,652,142× 3,415,983× 3,952,975× 5,347,924× 5,093,867× 4,556,660× 3,746,891× 3,687,326× 4,092,401× 3,864,537× 2,580,565× 2,034,779× 1,676,818× 1,109,472× 1,352,250× 2,054,840× 911,132× 676,449× 363,455× 618,974× 676,267× 627,980× 307,155× 277,485× 237,472× 434,985× 458,604× 382,052× 281,181× 85,300× 119,060× 19,530× 90,378× 41,842× 116,150× 78,786× 32,484× 163,450× 502,888× 352,214× 321,337× 126,935× 49,531× 18,019× 56,803× 40,340× 12,050× 16,063× 15,893× 38,286× 5,140× |