| 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 | 9.06 step avg | 10.87 step avg | 9.79 step avg | 14.06 step avg | 46.60 step avg | 25.99 step avg | 238.97 step avg | 36.90 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 43× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 0× 2× 72× 66× 102× 140× 92× 0× 0× 0× 0× 0× 6× 250× 260× | 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: 0× 1× 549× 504× 1,006× 998× 986× 970× 950× 926× 898× 866× 830× 790× 746× 698× 646× 590× 530× 466× 398× 326× 250× 170× 86× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 0× 1× 43× 0× 0× 0× 2,400× 5,240× 21,120× 84,480× 14,544× 13,125× 24,288× 4,292× 3,120× 5,712× | 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: 0× 1× 43× 1,472× 506× 14,340× 20,488× 23,750× 54,764× 73,596× 114,214× 148,970× 169,100× 154,020× 194,104× 154,126× 140,980× 125,476× 99,434× 76,232× 46,960× 38,330× 29,288× 19,662× 11,442× 1,006× | 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: 0× 1× 2,749× 11,454× 17,010× 9,388× 32,176× 16,774× 8,972× 15,319× 14,558× 14,666× 41,970× 61,465× 121,274× 160,382× 150,385× 138,809× 133,955× 79,551× 144,718× 161,306× 182,144× 139,614× 160,204× 192,093× 185,145× 216,895× 205,302× 236,338× 273,787× 315,830× 340,045× 315,864× 309,485× 305,918× 306,526× 293,564× 293,145× 297,873× 273,922× 215,991× 279,528× 289,573× 305,474× 270,758× 242,519× 263,477× 271,751× 206,659× 250,392× 221,688× 239,302× 224,878× 251,430× 182,706× 121,028× 141,370× 120,910× 113,085× 128,418× 143,788× 118,859× 118,630× 108,478× 109,032× 112,691× 102,423× 146,244× 138,024× 147,136× 94,791× 130,248× 112,443× 108,868× 125,636× 132,091× 124,157× 148,380× 142,313× 155,136× 136,566× 79,000× 59,712× 56,816× 48,784× 49,076× 59,886× 40,444× 44,206× 38,470× 37,729× 34,751× 34,789× 25,290× 36,946× 53,730× 44,110× 15,058× 22,447× 5,364× 17,916× 1,845× | 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: 0× 1× 19,051× 71,356× 195,828× 366,022× 560,776× 748,878× 877,250× 1,393,162× 1,892,254× 2,121,424× 2,112,104× 1,991,804× 1,063,578× 730,738× 220,742× 114,780× 4,752× 0× 351,296× 917,388× 1,804,662× 2,673,792× 3,870,530× 5,071,424× 6,888,544× 9,223,396× 10,577,834× 9,828,402× 9,426,938× 9,092,512× 7,063,126× 4,346,338× 1,953,434× 995,904× 751,848× 371,938× 141,418× 31,192× 17,984× | 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: 362s: 363s: 364s: 365s: 366s: 367s: 368s: 369s: 370s: 371s: 372s: 373s: 374s: 375s: 376s: 377s: 378s: 379s: 380s: 381s: 382s: 383s: 384s: 385s: 386s: 387s: 388s: 389s: 390s: 391s: 392s: 393s: 394s: 395s: 396s: 397s: 398s: 399s: 400s: 401s: 402s: 403s: 404s: 405s: 406s: 407s: 408s: 409s: 410s: 411s: 412s: 413s: 414s: 415s: 416s: 417s: 418s: 0× 1× 43× 0× 0× 0× 0× 0× 61,360× 254,920× 251,697× 151,836× 129,480× 317,827× 248,124× 205,705× 316,741× 218,882× 369,985× 411,500× 491,588× 567,690× 655,393× 953,312× 906,855× 694,643× 457,600× 325,057× 265,864× 146,915× 115,890× 183,242× 270,708× 250,808× 236,626× 194,236× 269,822× 264,015× 219,417× 174,347× 121,412× 170,046× 127,018× 70,111× 128,261× 87,931× 218,502× 236,740× 323,239× 326,440× 220,212× 351,055× 94,196× 18,320× 7,938× 4,648× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 521,885× 2,186,428× 2,536,024× 2,575,945× 2,799,999× 3,087,010× 2,586,956× 2,693,069× 3,302,989× 3,254,468× 3,167,677× 3,050,625× 3,007,698× 2,934,061× 2,744,636× 2,374,653× 2,494,778× 2,291,702× 2,128,751× 2,342,628× 2,698,394× 2,894,462× 2,772,501× 2,851,947× 3,521,209× 4,434,023× 3,941,727× 3,423,333× 2,854,190× 2,708,172× 3,147,269× 3,746,544× 3,496,168× 3,400,701× 2,889,373× 2,778,277× 3,110,206× 2,872,483× 2,715,961× 2,631,574× 2,500,878× 2,109,915× 1,933,606× 2,187,961× 2,468,718× 2,685,919× 2,996,380× 2,830,791× 2,829,215× 2,253,312× 2,218,326× 2,211,553× 2,554,205× 2,334,810× 2,257,839× 1,982,842× 2,003,442× 1,644,669× 1,526,295× 1,655,639× 1,586,342× 1,520,357× 1,506,575× 1,370,708× 1,296,777× 1,226,808× 1,053,237× 1,061,170× 776,643× 624,355× 711,214× 648,808× 889,318× 952,748× 947,471× 676,748× 697,740× 516,698× 385,525× 463,866× 603,626× 700,843× 619,206× 796,345× 1,104,403× 702,651× 1,027,786× 1,290,432× 1,911,976× 1,854,807× 1,944,353× 1,481,568× 1,743,730× 2,152,679× 2,320,693× 2,493,623× 2,293,632× 2,209,745× 2,729,827× 3,072,785× 2,886,844× 2,580,724× 2,639,614× 2,856,595× 3,172,160× 3,169,054× 3,384,034× 3,484,877× 3,987,622× 3,941,195× 3,749,969× 4,438,938× 4,579,712× 5,014,902× 4,749,144× 3,976,279× 3,746,780× 4,053,505× 4,347,338× 4,611,830× 3,935,521× 3,291,029× 4,011,857× 3,865,531× 3,651,600× 3,166,028× 3,518,067× 3,788,381× 4,186,889× 4,336,317× 4,375,906× 4,177,926× 3,995,854× 3,500,781× 3,431,542× 3,205,386× 3,699,566× 3,251,874× 3,232,517× 2,856,617× 2,140,607× 2,414,052× 2,723,971× 2,438,063× 2,681,357× 2,056,614× 2,189,061× 2,280,056× 2,067,070× 2,015,185× 2,087,016× 1,998,250× 1,873,960× 1,969,808× 2,258,538× 2,061,140× 1,906,900× 1,958,096× 2,197,432× 1,937,277× 1,591,896× 1,730,602× 1,429,424× 1,471,064× 1,262,724× 1,593,023× 1,987,866× 2,038,670× 2,234,200× 2,354,389× 2,844,059× 2,972,383× 2,695,389× 2,516,016× 2,516,988× 2,586,596× 2,321,968× 2,232,761× 1,880,335× 2,036,770× 2,054,683× 2,055,359× 2,160,360× 2,003,271× 1,923,714× 1,714,429× 1,885,766× 1,786,597× 1,607,631× 1,348,419× 1,697,352× 1,630,791× 2,086,769× 1,937,448× 2,229,762× 1,935,790× 1,720,147× 1,831,565× 2,005,384× 2,142,825× 2,178,924× 2,079,410× 1,574,999× 1,774,180× 1,941,875× 2,023,110× 1,990,972× 2,178,344× 2,306,724× 2,221,558× 2,375,946× 2,074,931× 1,795,176× 1,721,986× 1,784,237× 1,760,547× 1,951,736× 1,938,450× 1,765,342× 1,908,135× 1,623,702× 1,323,140× 1,254,855× 1,508,495× 1,536,838× 1,843,205× 1,819,703× 1,638,199× 1,672,490× 1,585,705× 1,631,288× 1,732,019× 1,549,302× 1,269,708× 1,260,101× 1,187,107× 1,512,668× 1,510,255× 1,375,298× 1,232,171× 1,190,777× 1,561,195× 1,882,682× 1,921,997× 1,666,875× 1,237,765× 1,229,946× 1,201,508× 1,355,925× 1,254,336× 1,343,309× 1,385,611× 1,232,326× 1,059,201× 968,625× 934,482× 1,046,821× 763,017× 964,437× 1,270,773× 1,377,704× 1,356,793× 1,290,606× 1,381,471× 1,624,771× 1,347,800× 1,503,250× 1,330,432× 1,637,358× 1,296,460× 896,196× 980,056× 1,207,090× 1,017,963× 949,181× 1,094,938× 1,160,179× 1,061,978× 1,293,471× 887,578× 1,021,504× 985,924× 1,281,736× 1,712,222× 1,567,702× 1,284,188× 842,220× 723,012× 699,525× 936,025× 956,889× 880,037× 958,729× 906,235× 749,933× 634,229× 863,766× 753,074× 521,782× 193,896× 311,239× 236,407× 270,169× 244,842× 180,741× 94,540× | 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: 0× 1× 157,365× 894,662× 2,659,358× 5,161,270× 10,587,268× 17,722,834× 28,593,392× 36,093,712× 34,218,630× 40,111,000× 36,495,386× 33,125,954× 26,340,434× 25,878,594× 18,884,312× 20,493,698× 15,880,518× 9,997,764× 7,224,920× 3,311,008× 520,156× 32,152× 1,774,178× 8,306,880× 19,417,880× 37,608,658× 66,254,140× 103,188,730× 145,772,424× 154,405,866× 165,508,798× 168,143,004× 151,573,646× 170,712,164× 177,521,604× 161,054,270× 164,495,722× 128,421,908× 135,900,582× 130,965,986× 145,190,638× 152,256,388× 144,089,066× 91,011,464× 69,710,956× 62,253,406× 60,827,938× 64,514,942× 60,287,218× 43,785,478× 24,675,680× 11,890,848× 11,404,738× 14,392,050× 26,799,908× 41,661,552× 51,110,340× 46,813,300× 39,651,260× 23,436,198× 11,750,946× 7,851,800× 4,619,646× 2,504,484× 1,048,036× 126,292× |