| 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 Cycle Start | 0.96 step avg | 1.43 step avg | 6.83 step avg | 6.15 step avg | 6.88 step avg | 18.81 step avg | 6.98 step avg | 34.78 step avg | 13.10 step avg | 37.16 step avg | 28.70 step avg | 75.00 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 27× | 0s: 1s: 2s: 8× 216× 182× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 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: 1× 379× 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: 1× 7,425× 10,340× 9,038× 17,300× 19,414× 23,708× 25,868× 25,526× 25,312× 15,514× 12,792× 7,008× 2,130× | 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: 1× 16,282× 38,257× 42,598× 45,177× 47,275× 46,075× 37,889× 45,246× 52,438× 46,470× 29,985× 31,382× 21,717× 24,688× 23,804× 24,684× 22,642× 18,207× 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: 1× 67,507× 155,354× 264,660× 442,770× 598,896× 673,964× 791,658× 839,672× 716,872× 469,980× 211,742× 89,996× 37,160× 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: 1× 47,567× 244,022× 298,480× 285,467× 370,455× 371,174× 363,126× 336,934× 364,014× 473,205× 423,306× 425,557× 349,028× 405,524× 444,060× 488,114× 504,920× 495,454× 472,952× 368,678× 310,356× 295,179× 303,930× 322,937× 377,161× 353,016× 361,081× 373,342× 375,174× 408,400× 372,980× 357,010× 352,771× 501,956× 564,975× 571,131× 621,285× 654,155× 547,585× 426,837× 365,061× 327,486× 356,849× 426,932× 315,500× 210,048× 190,505× 154,712× 141,108× 173,842× 163,835× 161,662× 203,129× 202,678× 181,790× 169,641× 200,435× 172,329× 151,827× 155,916× 134,211× 155,853× 165,295× 201,970× 129,962× 132,065× 135,163× 145,242× 144,871× 155,639× 128,362× 114,189× 92,202× 77,772× 83,575× 67,096× 52,696× 28,363× 37,291× 60,869× 42,672× 39,414× 28,245× 23,114× 17,180× 14,325× 11,428× 10,679× 3,652× 6,548× 4,656× 6,776× 7,226× 10,332× 9,954× 14,546× 8,006× 5,812× 10,034× 17,048× 30,076× 24,408× 35,540× 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: 1× 108,029× 461,072× 1,225,240× 2,202,176× 4,071,014× 5,635,028× 6,443,352× 6,495,622× 6,038,872× 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: 1× 386,476× 3,322,564× 5,301,712× 4,868,511× 5,090,799× 5,307,659× 6,247,449× 5,672,859× 5,260,457× 5,617,454× 4,879,341× 5,143,945× 5,937,096× 6,156,230× 6,168,898× 6,108,292× 6,309,240× 6,647,866× 6,534,885× 6,061,399× 5,271,890× 4,617,857× 4,652,532× 4,857,877× 5,449,933× 5,103,476× 4,492,896× 4,136,169× 4,462,978× 4,461,373× 4,630,381× 4,561,835× 5,207,564× 4,967,540× 5,228,611× 5,045,944× 4,861,007× 4,785,281× 5,294,205× 4,477,405× 4,464,414× 4,470,670× 4,543,565× 5,502,062× 5,464,102× 4,935,117× 4,686,174× 4,270,813× 4,302,476× 4,454,665× 4,119,838× 4,239,792× 3,531,113× 3,522,746× 3,396,132× 3,537,307× 3,727,205× 3,169,645× 2,920,597× 3,096,661× 3,066,259× 2,544,907× 2,561,899× 2,541,546× 2,801,854× 2,282,047× 1,673,415× 1,693,489× 2,093,039× 2,589,339× 2,853,432× 2,946,093× 2,999,221× 2,106,356× 1,678,550× 1,515,367× 1,674,497× 2,179,828× 1,837,042× 2,313,473× 1,759,615× 1,608,267× 1,172,961× 1,229,501× 996,488× 1,027,726× 1,119,376× 901,541× 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: 1× 787,657× 4,832,248× 12,384,504× 21,437,590× 32,070,164× 43,035,960× 40,543,430× 37,299,698× 31,240,162× 27,237,698× 29,221,492× 30,112,150× 38,159,620× 35,675,170× 35,974,344× 27,633,072× 23,980,120× 22,662,412× 17,923,982× 15,216,088× 12,161,386× 10,766,846× 13,142,592× 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: 1× 338,837× 8,139,616× 16,486,988× 13,242,225× 17,239,233× 15,260,843× 16,374,917× 19,380,808× 21,942,902× 24,425,391× 20,346,135× 18,762,540× 23,261,265× 30,380,852× 40,653,760× 46,400,169× 38,332,747× 38,752,444× 47,270,703× 55,744,793× 47,137,659× 42,084,203× 41,629,563× 39,767,778× 50,374,589× 50,018,416× 40,847,540× 35,901,026× 36,926,845× 40,954,334× 49,755,132× 45,534,838× 44,507,054× 35,270,894× 35,433,361× 38,498,852× 40,655,343× 40,944,716× 37,089,347× 43,919,856× 43,198,944× 38,869,991× 43,302,686× 41,492,765× 40,908,280× 44,300,816× 44,087,701× 53,384,408× 53,153,601× 51,185,507× 45,926,961× 40,930,130× 39,463,245× 39,016,183× 36,911,119× 37,423,088× 37,539,446× 39,767,507× 35,401,006× 35,883,532× 31,739,366× 26,228,818× 22,902,761× 23,755,004× 24,616,958× 25,702,853× 28,004,784× 23,564,860× 22,978,236× 19,894,235× 18,655,605× 14,421,953× 13,631,003× 13,207,251× 16,116,632× 13,809,403× 10,197,401× 10,664,952× 10,727,828× 11,492,731× 12,175,100× 9,098,309× 6,840,144× 6,233,109× 7,057,206× 7,104,146× 7,305,225× 8,684,130× 10,176,933× 9,184,325× 11,777,871× 15,078,173× 15,473,309× 14,547,253× 10,565,264× 7,500,683× 6,056,345× 5,208,340× 6,867,979× 7,662,723× 8,077,770× 9,379,347× 8,840,928× 8,914,945× 8,556,654× 11,142,142× 8,920,270× 8,304,641× 8,566,770× 10,741,634× 9,675,475× 8,502,687× 6,666,409× 6,195,905× 6,694,204× 10,675,213× 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× |