| 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 |
|---|---|---|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.98 step avg | 8.17 step avg | 10.49 step avg | 8.55 step avg | 12.89 step avg | 72.86 step avg | 18.48 step avg | 168.58 step avg | 26.23 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 41× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 41× 0× 0× 0× 0× 11× 430× 420× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 0× 1× 503× 460× 918× 910× 898× 882× 862× 838× 810× 778× 742× 702× 658× 610× 558× 502× 442× 378× 310× 238× 162× 82× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 0× 1× 41× 0× 1,964× 4,434× 17,388× 8,333× 19,044× 69,552× 13,364× 11,057× 2,169× 1,648× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 0× 1× 3,191× 6,666× 8,768× 18,506× 29,862× 52,704× 77,228× 88,752× 88,134× 134,858× 121,818× 124,424× 131,224× 125,004× 96,978× 84,194× 65,722× 53,196× 38,088× 16,998× 4,438× | 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: 0× 1× 503× 0× 0× 0× 0× 5,728× 32,596× 75,627× 56,328× 47,475× 49,582× 60,302× 53,012× 69,392× 62,448× 62,091× 46,640× 54,415× 36,506× 32,511× 47,749× 59,056× 62,314× 63,944× 43,196× 44,164× 36,432× 38,246× 16,481× 5,376× 1,748× 5,312× 8,766× 5,384× 0× 0× 0× 0× 0× 0× 0× 0× 39,199× 111,775× 118,723× 110,788× 113,310× 108,583× 128,164× 129,845× 133,820× 109,032× 118,460× 133,236× 119,503× 127,916× 118,416× 103,637× 136,296× 163,039× 140,031× 127,570× 126,131× 121,638× 106,435× 143,247× 156,434× 186,490× 158,245× 134,058× 174,760× 162,528× 198,691× 188,770× 174,140× 178,595× 154,866× 136,052× 173,547× 135,082× 117,734× 153,589× 152,415× 183,059× 198,366× 213,182× 189,075× 177,365× 164,884× 132,309× 125,417× 123,770× 139,364× 99,134× 84,096× 106,417× 140,114× 122,992× 150,663× 128,282× 85,783× 84,284× 69,984× 68,328× 89,979× 91,519× 63,607× 52,649× 69,293× 69,709× 72,941× 62,957× 53,418× 68,032× 59,121× 59,686× 51,623× 45,312× 16,664× 14,126× 22,134× 17,722× 42,768× 33,297× 32,464× 26,055× 6,354× 10,320× 10,840× | 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: 0× 1× 41× 0× 0× 62,084× 166,628× 357,780× 515,378× 672,844× 831,402× 1,244,846× 1,875,498× 2,816,890× 3,953,402× 4,784,488× 5,043,406× 5,777,264× 5,661,154× 6,458,058× 7,198,514× 8,076,418× 6,874,610× 4,905,870× 3,339,148× 1,876,332× 616,886× 281,062× 146,770× 87,098× 5,200× | 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: 0× 1× 14,489× 59,622× 110,842× 96,830× 193,450× 121,190× 127,986× 97,118× 103,964× 89,698× 69,703× 41,132× 109,468× 380,106× 336,077× 290,324× 241,369× 281,054× 189,924× 176,218× 101,993× 58,672× 71,986× 61,514× 72,245× 65,229× 41,012× 38,580× 50,596× 98,032× 140,766× 19,515× 11,704× 0× 0× 0× 0× 0× 0× 0× 148,455× 732,075× 786,080× 908,620× 909,841× 604,102× 484,842× 634,940× 431,980× 371,368× 473,180× 652,865× 726,653× 529,365× 558,459× 852,735× 1,089,828× 1,162,579× 1,157,439× 1,296,999× 985,316× 1,275,893× 1,121,701× 942,246× 916,609× 834,299× 880,165× 777,548× 1,034,252× 1,639,645× 1,667,279× 1,468,934× 1,385,196× 1,383,405× 1,191,050× 1,490,064× 1,531,526× 1,753,409× 1,402,761× 1,612,865× 1,378,784× 1,089,956× 1,090,195× 1,177,445× 1,457,885× 1,584,412× 1,516,581× 1,319,871× 1,568,409× 1,458,367× 1,270,869× 1,055,050× 1,097,592× 1,296,217× 1,347,199× 1,214,199× 1,036,649× 1,040,771× 1,112,068× 901,609× 892,434× 786,236× 832,656× 871,669× 692,453× 503,553× 592,083× 448,170× 584,483× 901,353× 993,726× 718,292× 709,214× 674,344× 787,850× 720,106× 566,393× 517,597× 679,696× 769,359× 742,742× 1,023,304× 727,591× 799,260× 677,224× 795,932× 1,013,952× 967,140× 895,043× 798,367× 831,710× 989,180× 1,165,949× 1,201,233× 1,153,885× 1,010,059× 975,561× 883,009× 820,127× 1,154,247× 1,251,238× 902,230× 995,104× 1,924,282× 4,178,769× 4,238,287× 4,859,773× 4,657,463× 4,670,392× 4,299,182× 4,306,334× 4,641,639× 3,883,169× 3,217,462× 3,481,757× 3,162,976× 3,381,265× 3,273,458× 3,317,361× 3,379,231× 3,486,779× 2,704,935× 2,843,747× 2,624,768× 2,877,274× 3,216,063× 3,463,202× 3,852,386× 4,081,645× 4,091,702× 3,885,116× 3,441,992× 3,964,003× 3,927,650× 3,780,754× 4,251,555× 4,263,289× 4,109,461× 4,406,745× 3,965,743× 3,395,879× 3,657,938× 3,975,519× 3,775,677× 4,291,395× 5,054,191× 5,139,818× 4,850,177× 4,780,320× 4,706,111× 4,448,867× 4,016,848× 3,925,513× 4,289,362× 4,348,946× 4,657,664× 4,209,525× 4,128,378× 4,196,548× 5,328,319× 5,522,740× 4,723,282× 3,876,489× 3,693,523× 3,675,731× 3,776,243× 3,822,208× 3,690,463× 3,651,645× 3,497,454× 3,374,691× 2,918,108× 2,807,782× 2,604,645× 2,391,698× 2,142,574× 2,195,261× 2,268,040× 2,294,082× 2,211,724× 1,770,330× 1,777,313× 1,728,456× 1,721,278× 1,674,165× 1,839,596× 1,749,562× 1,418,732× 1,378,512× 1,316,612× 1,448,020× 1,364,891× 1,551,076× 1,884,231× 2,173,307× 1,854,355× 1,412,063× 1,028,085× 1,175,327× 1,262,498× 1,130,024× 1,243,847× 1,150,037× 962,348× 744,029× 804,499× 631,891× 663,416× 646,572× 777,951× 996,123× 850,560× 646,492× 742,082× 428,331× 254,302× 240,583× 261,471× 129,790× 98,034× 99,529× 198,745× 154,868× 135,297× 164,477× 175,214× 223,581× 246,842× 427,115× 255,619× 212,492× 129,546× 161,902× 226,019× 325,381× 308,948× 277,647× 255,589× 306,339× 263,538× 284,053× 427,903× 364,172× 345,258× 351,366× 441,625× 640,885× 505,165× 592,529× 377,280× 409,074× 303,233× 186,251× 189,560× 155,709× 280,728× 107,860× 48,138× 82,266× 81,792× 56,740× 29,586× 11,568× | 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: 0× 1× 64,655× 603,700× 2,479,990× 6,622,184× 15,115,198× 23,431,476× 39,137,820× 49,634,308× 53,888,494× 63,481,886× 77,556,168× 89,159,538× 76,509,622× 63,516,250× 50,184,450× 53,365,704× 59,867,876× 69,707,328× 83,224,222× 95,442,158× 97,933,084× 100,577,140× 85,230,670× 68,558,412× 45,290,824× 30,360,068× 30,866,662× 44,842,374× 44,129,790× 49,425,236× 44,346,494× 41,418,870× 43,400,616× 46,443,238× 62,019,156× 75,323,776× 104,219,160× 98,953,120× 113,903,410× 96,695,830× 75,313,336× 55,546,502× 36,239,032× 21,494,170× 12,524,118× 5,189,592× 1,669,928× 437,740× 88,324× |