| 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 |
| 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 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.96 step avg | 14.53 step avg | 7.83 step avg | 9.15 step avg | 10.22 step avg | 45.29 step avg | 23.72 step avg | 50.25 step avg | 22.98 step avg | 136.51 step avg | 39.61 step avg | 96.49 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 27× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 0× 1× 27× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 7× 189× 182× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 0× 1× 237× 208× 414× 406× 394× 378× 358× 334× 306× 274× 238× 198× 154× 106× 54× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 0× 1× 27× 0× 352× 660× 2,688× 10,752× 3,128× 2,903× 5,394× 760× 268× 526× 640× 324× 568× 432× 738× 1,304× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 0× 1× 27× 600× 3,096× 8,374× 9,616× 12,984× 17,878× 20,858× 29,922× 29,136× 27,296× 18,904× 13,304× 7,196× 2,184× | 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: 0× 1× 237× 0× 1,088× 3,278× 2,608× 2,848× 3,254× 3,722× 9,338× 12,123× 11,946× 13,510× 11,844× 15,075× 15,366× 12,602× 8,996× 9,840× 12,364× 5,613× 6,902× 7,322× 5,269× 2,884× 2,644× 0× 0× 0× 0× 10,178× 20,650× 26,008× 29,259× 26,804× 31,821× 24,413× 31,102× 38,847× 31,704× 25,046× 25,674× 16,339× 20,775× 19,768× 20,434× 19,758× 15,563× 15,821× 9,445× 12,040× 18,746× 28,141× 26,981× 35,384× 28,001× 27,667× 26,874× 22,335× 19,513× 11,260× 12,495× 16,351× 11,996× 8,071× 9,999× 8,556× 14,073× 11,424× 16,208× 15,778× 14,647× 16,586× 12,656× 14,508× 10,328× 4,955× 3,916× 4,022× 3,750× 224× | 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: 0× 1× 3,611× 13,320× 26,546× 58,372× 66,366× 84,754× 131,736× 160,430× 91,180× 21,398× 13,704× 4,092× 1,140× 0× 0× 0× 0× 0× 63,896× 142,034× 238,114× 384,398× 532,530× 589,210× 659,922× 679,242× 625,692× 448,582× 198,038× 85,904× 36,020× 17,646× 1,738× | 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: 0× 1× 1,307× 2,230× 4,660× 24,928× 18,484× 19,259× 27,089× 44,216× 61,095× 57,709× 57,910× 96,620× 116,902× 132,256× 108,832× 128,569× 151,030× 138,661× 166,616× 176,419× 212,640× 229,195× 221,870× 225,582× 230,408× 239,370× 200,123× 161,371× 169,715× 165,060× 208,550× 372,322× 394,755× 362,482× 503,915× 559,317× 635,200× 576,935× 550,051× 604,954× 696,031× 718,604× 705,806× 777,510× 814,946× 709,406× 623,053× 510,805× 466,519× 452,279× 554,514× 433,582× 327,547× 274,316× 273,349× 268,297× 306,187× 258,368× 180,042× 189,356× 199,857× 203,644× 174,133× 238,494× 195,740× 194,746× 208,757× 181,837× 203,367× 184,024× 225,947× 148,927× 166,053× 158,106× 163,604× 169,542× 188,504× 145,230× 111,718× 96,399× 77,050× 114,446× 131,631× 111,295× 86,937× 91,639× 95,317× 76,698× 64,648× 59,732× 60,722× 55,767× 60,332× 52,142× 42,579× 23,448× 13,377× 7,078× 8,494× 12,940× 29,674× 39,791× 52,348× 47,856× 28,302× 12,476× 23,552× 32,384× 26,700× 35,832× 25,018× 25,142× 25,801× 38,031× 42,378× 44,854× 8,321× 12,666× 5,738× 6,278× 15,060× 26,517× 29,509× 17,436× 17,360× 12,958× 12,513× 17,397× 13,178× 14,258× 12,148× 8,416× 12,736× 14,902× 25,416× 18,564× 284× | 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: 0× 1× 9,957× 48,920× 133,050× 113,022× 300,958× 233,118× 321,250× 85,706× 8,448× 98,072× 412,152× 1,092,190× 2,089,154× 3,770,056× 5,401,910× 6,122,102× 6,409,916× 6,030,424× 6,010,506× 4,973,302× 5,519,334× 5,213,210× 4,386,846× 4,282,562× 3,918,230× 4,654,308× 4,547,098× 3,750,706× 2,432,296× 1,461,946× 1,379,510× 1,295,272× 1,152,350× 1,508,462× 1,264,900× 1,350,276× 971,056× 315,012× 325,888× 295,102× 216,134× 44,638× 87,140× 42,788× 58,568× 5,434× | 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: 0× 1× 1,947× 6,130× 17,308× 208,000× 323,307× 316,461× 466,379× 567,751× 451,041× 434,769× 492,014× 661,092× 855,841× 646,252× 698,723× 836,945× 989,457× 846,959× 744,509× 522,698× 465,462× 557,085× 476,883× 501,373× 361,632× 287,049× 470,358× 585,567× 935,032× 1,102,495× 1,014,217× 1,037,077× 816,621× 669,717× 558,261× 705,338× 799,799× 573,976× 650,271× 579,816× 524,566× 536,594× 477,461× 319,541× 372,097× 386,305× 427,950× 345,913× 288,833× 305,444× 504,607× 412,149× 477,536× 235,655× 271,808× 610,617× 580,050× 536,698× 332,407× 218,658× 147,697× 210,990× 338,652× 314,108× 234,180× 214,192× 261,038× 198,086× 142,986× 216,037× 289,702× 386,697× 327,779× 456,556× 408,015× 171,502× 118,822× 80,693× 208,361× 319,521× 383,982× 491,505× 511,635× 442,202× 189,399× 95,328× 30,190× 21,303× 3,122× 432× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 275,701× 2,451,400× 4,017,013× 3,628,461× 3,750,252× 4,182,176× 5,325,102× 4,978,638× 4,576,537× 4,928,433× 4,153,318× 4,693,917× 5,416,052× 5,424,926× 5,324,253× 5,334,632× 5,569,014× 6,143,026× 6,094,839× 5,534,524× 4,797,203× 4,120,470× 4,311,806× 4,587,802× 5,003,581× 4,591,517× 4,035,553× 3,738,692× 4,105,103× 4,078,200× 4,253,433× 4,190,368× 4,816,592× 4,452,794× 4,610,216× 4,574,994× 4,247,019× 4,245,854× 4,778,071× 3,948,149× 3,988,843× 4,152,722× 4,171,468× 5,115,757× 5,036,152× 4,589,204× 4,397,341× 3,965,369× 3,797,869× 4,042,516× 3,642,302× 4,004,137× 3,259,305× 2,912,129× 2,816,082× 3,000,609× 3,394,798× 2,950,987× 2,772,900× 2,885,671× 2,727,607× 2,230,799× 2,327,719× 2,327,354× 2,540,816× 2,083,961× 1,530,429× 1,477,452× 1,803,337× 2,202,642× 2,525,653× 2,489,537× 2,591,206× 1,934,854× 1,559,728× 1,434,674× 1,466,136× 1,860,307× 1,453,060× 1,821,968× 1,247,980× 1,166,065× 983,562× 1,134,173× 966,298× 1,006,423× 1,116,254× 901,109× 813,373× 643,570× 452,924× 422,418× 386,603× 295,431× 387,285× 460,799× 598,132× 385,096× 213,810× 160,745× 195,350× 179,703× 218,815× 144,146× 56,554× 56,428× 92,425× 111,205× 137,675× 155,189× 19,107× 12,487× 7,778× 4,232× 6,747× | 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: 0× 1× 27,027× 206,010× 892,190× 2,094,996× 5,003,738× 9,336,544× 13,305,024× 17,845,326× 13,082,944× 9,718,574× 7,558,182× 7,514,706× 11,279,546× 9,536,440× 9,607,282× 9,610,198× 12,598,246× 10,880,714× 13,634,808× 15,931,886× 25,586,556× 34,812,388× 48,022,854× 53,979,776× 48,848,458× 38,401,814× 31,698,416× 28,860,676× 20,893,488× 16,402,588× 12,407,970× 10,776,296× 13,142,724× 10,488,776× 9,052,942× 8,984,022× 11,572,874× 12,614,986× 14,494,778× 13,733,108× 13,799,652× 16,144,312× 17,862,390× 16,033,572× 16,852,100× 14,802,070× 17,564,782× 15,888,202× 21,003,030× 24,956,396× 26,002,074× 25,584,610× 27,572,336× 31,072,870× 30,222,560× 27,340,132× 24,193,878× 18,806,730× 10,739,490× 6,593,990× 4,744,484× 6,603,156× 5,086,688× 5,172,702× 6,225,576× 10,603,490× 15,448,504× 23,791,232× 14,808,264× 9,843,492× 7,468,694× 6,426,042× 5,245,910× 5,678,052× 8,214,092× 9,937,628× 5,681,980× 2,837,870× 1,635,966× 306,560× 54,330× 32,528× | 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: 0× 1× 2,157× 9,970× 86,224× 2,202,468× 4,828,213× 4,099,711× 6,663,833× 6,994,074× 5,321,696× 7,808,319× 9,910,268× 9,781,859× 8,092,878× 6,939,948× 8,155,666× 10,473,200× 14,464,254× 15,478,334× 12,390,469× 12,200,149× 12,746,290× 14,983,102× 14,648,942× 14,945,118× 12,539,304× 12,965,397× 17,747,642× 21,590,805× 17,184,798× 17,306,961× 15,035,051× 16,388,935× 21,309,827× 22,006,938× 22,003,401× 16,988,700× 17,006,185× 19,271,728× 25,633,316× 33,565,393× 36,553,035× 30,984,997× 34,378,119× 44,754,044× 51,717,607× 45,510,643× 43,481,391× 45,446,317× 45,853,349× 52,793,767× 54,506,903× 48,573,636× 43,311,191× 43,259,061× 49,466,328× 58,016,556× 51,286,964× 50,264,792× 40,782,541× 33,697,606× 36,442,783× 39,416,607× 42,479,210× 40,341,325× 44,574,959× 42,985,203× 37,400,205× 41,821,502× 39,895,169× 37,371,854× 40,645,281× 38,514,462× 43,763,639× 44,741,252× 41,757,774× 40,318,027× 39,116,117× 33,701,683× 31,927,317× 27,168,248× 26,086,565× 24,882,850× 28,610,918× 26,052,579× 24,339,145× 18,718,624× 17,108,038× 15,966,032× 16,321,818× 18,136,035× 20,706,461× 20,980,444× 17,768,033× 17,264,293× 15,171,451× 13,698,019× 10,182,037× 9,061,539× 10,316,565× 11,550,426× 10,934,724× 8,466,099× 8,794,027× 9,292,243× 9,647,330× 9,757,207× 7,088,577× 5,439,206× 5,892,100× 6,726,640× 5,696,201× 5,859,424× 7,521,684× 7,944,390× 7,157,760× 8,503,400× 11,753,116× 12,362,638× 12,086,436× 9,358,423× 6,820,898× 5,162,148× 4,415,916× 5,496,232× 7,044,985× 7,502,216× 8,904,855× 8,560,805× 8,690,827× 8,468,134× 10,933,978× 8,272,355× 7,488,981× 8,404,842× 10,631,360× 9,575,936× 8,372,743× 6,595,315× 6,194,963× 6,692,754× 10,672,898× 16,028,000× 18,151,213× 18,687,643× 16,345,157× 13,824,422× 9,479,868× 9,907,023× 10,252,025× 11,735,167× 10,733,972× 11,969,364× 14,031,850× 15,067,715× 13,853,744× 12,068,755× 14,081,154× 11,502,923× 11,626,585× 12,803,945× 9,343,214× 9,256,053× 7,069,995× 6,963,241× 8,382,258× 7,565,913× 7,748,116× 9,071,685× 12,390,690× 14,777,606× 13,752,792× 14,277,508× 10,867,485× 8,051,084× 9,126,948× 9,212,937× 13,246,123× 14,862,360× 15,351,561× 20,094,852× 23,322,111× 19,325,973× 19,125,587× 15,712,772× 10,826,658× 10,819,565× 9,591,363× 11,184,517× 14,526,265× 13,888,055× 11,398,810× 10,564,231× 12,406,314× 12,808,401× 10,275,572× 7,280,208× 6,977,721× 7,606,265× 9,187,262× 9,914,339× 9,072,196× 8,103,104× 8,416,982× 6,740,543× 9,231,493× 10,066,494× 12,759,890× 12,407,612× 11,802,933× 8,500,720× 6,717,117× 7,537,700× 8,196,785× 10,983,824× 13,957,721× 11,576,160× 10,644,058× 10,488,848× 9,231,111× 7,464,522× 7,262,279× 7,477,147× 7,488,969× 6,642,775× 3,893,897× 2,925,000× 3,663,805× 5,133,818× 6,253,382× 5,992,089× 5,225,898× 3,257,276× 2,597,218× 2,663,693× 2,394,787× 3,120,543× 2,967,185× 1,481,779× 1,262,454× 1,391,694× 1,260,940× 1,433,055× 1,033,043× 1,147,662× 2,608,777× 2,101,129× 1,495,086× 1,486,519× 860,546× 353,448× 246,989× 134,745× 128,023× 161,134× 125,136× 21,142× |