| Radix Character Encoding | ||||||
|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| 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 | # Full Cycles (excluding zero) |
Nodes | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | ||
| 1 | 0 cycles | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 2 | 0 cycles | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 3 | 1 cycle | - | 77× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 4 | 1 cycle | - | - | 203× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 5 | 1 cycle | - | - | - | - | 455× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 6 | 1 cycle | - | - | - | - | - | 917× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 7 | 1 cycle | - | - | - | - | - | 1,709× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 8 | 1 cycle | - | - | - | - | - | 2,996× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 9 | 1 cycle | - | - | - | - | - | - | - | - | - | - | 4,998× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 10 | 3 cycles | - | 8,001× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 11 | 1 cycle | 12,369× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 12 | 2 cycles | - | 3,858× | - | - | 14,699× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 13 | 3 cycles | 6,963× | - | - | - | - | 20,162× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 14 | 2 cycles | - | 19,508× | - | - | - | - | - | - | 19,245× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 15 | 4 cycles | 29,102× | 25,155× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 16 | 2 cycles | - | 44,585× | - | - | - | - | - | - | - | - | - | 30,021× | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 17 | 5 cycles | 66,533× | 34,407× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 18 | 1 cycle | - | 134,589× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 19 | 8 cycles | 62,520× | 65,202× | - | 49,371× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 20 | 6 cycles | 16,846× | 68,638× | - | - | 99,244× | - | 45,495× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 21 | 10 cycles | 79,197× | 99,793× | 117,013× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 22 | 5 cycles | 27,897× | 63,074× | - | - | 285,762× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 23 | 13 cycles | 138,417× | 152,529× | 184,067× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 24 | 7 cycles | 65,829× | 61,654× | - | - | 466,285× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 25 | 18 cycles | 360,474× | 222,520× | 153,280× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 26 | 7 cycles | 94,310× | 81,457× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 730,418× | - |
| 27 | 20 cycles | 233,071× | 313,102× | 561,388× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 28 | 8 cycles | 193,051× | 118,805× | - | - | - | - | 1,033,041× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 29 | 25 cycles | 369,712× | 433,371× | 820,070× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 30 | 12 cycles | 302,393× | 162,033× | 17,847× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 1,465,512× |
| 31 | 30 cycles | 491,724× | 531,038× | 1,302,015× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 32 | 13 cycles | 430,000× | 575,380× | 9,846× | - | - | - | - | - | - | - | - | - | 1,745,448× | - | - | - | - | - | - | - | - | - | - | - | - |
| 33 | 35 cycles | 668,868× | 754,979× | 1,838,769× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 34 | 15 cycles | 442,269× | 674,866× | 9,846× | - | - | - | - | - | - | - | - | - | 2,711,392× | - | - | - | - | - | - | - | - | - | - | - | - |
| 35 | 43 cycles | 852,576× | 885,323× | 2,357,629× | - | 400,853× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 36 | 16 cycles | 3,656,092× | 1,579,841× | 9,846× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 37 | 51 cycles | 998,529× | 1,175,478× | 3,140,412× | - | 782,028× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 38 | 20 cycles | 1,687,106× | 1,568,138× | 9,846× | - | - | - | - | - | - | - | - | - | - | - | - | - | 3,793,955× | - | - | - | - | - | - | - | - |
| 39 | 56 cycles | 1,335,806× | 1,410,284× | 3,862,758× | - | 1,536,205× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 40 | 25 cycles | 1,697,519× | 3,508,956× | 4,160,337× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 41 | 63 cycles | 1,717,296× | 1,699,181× | 4,539,570× | - | 1,966,733× | 814,786× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 42 | 29 cycles | 3,357,426× | 3,323,024× | 110,558× | - | - | - | - | - | - | - | 5,480,497× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 43 | 71 cycles | 1,959,483× | 1,974,819× | 5,830,389× | - | 2,690,220× | 1,528,898× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 44 | 33 cycles | 3,525,647× | 4,477,436× | 7,887,610× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 45 | 79 cycles | 2,356,686× | 2,362,522× | 7,023,830× | - | 3,282,638× | 2,983,777× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 46 | 38 cycles | 4,765,063× | 5,334,207× | 8,563,387× | - | - | - | 1,695,856× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 47 | 89 cycles | 3,013,102× | 3,537,421× | 8,380,624× | 348,667× | 4,312,188× | 3,365,471× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 48 | 42 cycles | 7,524,604× | 6,989,954× | 11,312,600× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 49 | 99 cycles | 3,737,890× | 4,472,993× | 9,891,017× | 609,984× | 5,129,396× | 5,148,388× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 50 | 48 cycles | 7,423,860× | 9,131,705× | 15,912,864× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 51 | 112 cycles | 5,618,052× | 5,304,470× | 11,950,861× | 1,045,941× | 6,585,645× | 5,783,276× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 52 | 53 cycles | 8,893,298× | 13,466,503× | 18,115,550× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 53 | 123 cycles | 5,552,980× | 5,994,648× | 14,105,656× | 4,063,892× | 7,705,807× | 7,634,484× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 54 | 57 cycles | 11,278,208× | 11,635,489× | 27,150,156× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 55 | 137 cycles | 6,701,521× | 7,159,626× | 16,042,166× | 7,397,082× | 9,510,949× | 8,714,021× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 56 | 63 cycles | 23,989,100× | 14,417,351× | 23,068,061× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 57 | 150 cycles | 7,893,177× | 8,824,871× | 18,254,073× | 10,628,357× | 10,991,438× | 11,353,598× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 58 | 71 cycles | 20,062,890× | 15,951,652× | 38,959,819× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 59 | 164 cycles | 9,206,310× | 9,772,164× | 21,673,203× | 13,309,787× | 12,797,248× | 13,167,430× | - | - | 2,672,731× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 60 | 79 cycles | 20,430,967× | 18,693,604× | 51,734,190× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 61 | 177 cycles | 10,658,894× | 11,350,215× | 24,649,517× | 17,615,486× | 15,254,661× | 15,271,099× | - | - | 4,995,817× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 62 | 87 cycles | 23,505,082× | 44,890,039× | 41,058,216× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 63 | 190 cycles | 12,719,912× | 13,421,507× | 27,886,419× | 20,371,997× | 17,887,841× | 17,515,916× | - | - | 10,073,873× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 64 | 95 cycles | 28,662,631× | 47,336,811× | 48,341,493× | - | - | - | - | - | - | - | 6,775,043× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 65 | 210 cycles | 14,716,051× | 15,346,787× | 32,842,477× | 25,428,888× | 19,548,724× | 23,739,376× | - | - | 11,596,689× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 66 | 101 cycles | 32,203,564× | 67,467,589× | 56,567,748× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 67 | 229 cycles | 16,901,286× | 18,539,138× | 38,334,623× | 29,121,120× | 22,640,037× | 27,420,003× | - | - | 17,274,238× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 68 | 109 cycles | 35,994,956× | 71,107,170× | 68,589,939× | - | 9,558,714× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 69 | 246 cycles | 19,493,409× | 19,863,228× | 45,316,860× | 36,744,476× | 26,932,892× | 33,440,597× | - | - | 19,568,081× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 70 | 119 cycles | 41,975,645× | 93,215,443× | 71,068,895× | - | 12,358,950× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 71 | 263 cycles | 21,775,999× | 22,325,767× | 50,821,566× | 42,561,772× | 29,213,080× | 37,775,959× | - | - | 27,279,025× | - | 5,340,605× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 72 | 132 cycles | 47,154,828× | 90,443,446× | 85,730,340× | - | 33,522,974× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 73 | 280 cycles | 24,715,600× | 24,738,762× | 58,159,494× | 49,027,439× | 32,775,881× | 47,089,845× | - | - | 31,326,081× | - | 10,129,576× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 74 | 141 cycles | 70,519,160× | 103,964,889× | 92,462,972× | - | 33,553,172× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 75 | 300 cycles | 28,080,822× | 27,444,493× | 68,146,613× | 56,034,840× | 36,997,668× | 51,278,278× | - | - | 39,213,486× | - | 17,344,009× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 76 | 151 cycles | 82,478,223× | 111,227,153× | 108,232,872× | - | 45,777,372× | - | - | - | 2,446,185× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 77 | 321 cycles | 32,455,407× | 32,642,590× | 75,361,441× | 65,423,738× | 40,925,641× | 59,523,203× | - | - | 43,669,254× | 6,524,771× | 20,921,096× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 78 | 161 cycles | 105,682,796× | 127,980,546× | 124,443,550× | - | 48,374,645× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 79 | 343 cycles | 36,404,415× | 37,285,721× | 83,856,984× | 72,320,141× | 45,606,239× | 65,894,040× | - | - | 53,368,370× | 11,275,638× | 31,342,005× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 80 | 172 cycles | 118,461,082× | 146,115,843× | 132,406,546× | - | 61,394,542× | 11,777,057× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 81 | 362 cycles | 41,677,394× | 41,565,541× | 94,423,550× | 81,820,189× | 49,924,102× | 76,499,211× | - | - | 59,372,995× | 24,165,391× | 35,532,999× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 82 | 185 cycles | 145,367,791× | 170,654,831× | 145,448,651× | - | 63,720,382× | 16,739,574× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 83 | 384 cycles | 46,564,440× | 47,378,912× | 105,039,008× | 91,275,084× | 55,223,724× | 83,968,629× | - | - | 78,667,006× | 23,350,311× | 49,639,867× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 84 | 195 cycles | 160,417,409× | 182,052,266× | 164,288,392× | - | 79,856,409× | 36,000,147× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 85 | 408 cycles | 51,851,765× | 52,831,871× | 119,291,250× | 103,984,635× | 60,829,063× | 95,392,395× | - | - | 90,287,942× | 37,038,376× | 55,056,594× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 86 | 210 cycles | 187,974,935× | 201,214,899× | 197,846,465× | - | 88,217,055× | 37,814,995× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 87 | 433 cycles | 61,984,750× | 60,232,540× | 130,909,208× | 113,650,004× | 67,110,296× | 104,625,234× | - | - | 113,687,034× | 41,816,667× | 68,229,744× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 88 | 221 cycles | 213,007,162× | 213,274,337× | 225,317,494× | - | 99,729,991× | 62,887,776× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 89 | 456 cycles | 65,197,540× | 66,950,316× | 146,658,899× | 126,493,579× | 73,312,795× | 119,705,461× | - | - | 126,801,293× | 55,628,436× | 74,333,707× | - | - | 14,025,752× | - | - | - | - | - | - | - | - | - | - | - |
| 90 | 234 cycles | 243,313,660× | 252,445,572× | 256,956,749× | - | 106,743,202× | 67,589,114× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 91 | 479 cycles | 73,554,663× | 72,241,619× | 163,601,365× | 140,205,425× | 79,769,811× | 129,125,712× | - | - | 154,395,459× | 61,224,128× | 89,125,483× | - | - | 24,928,696× | - | - | - | - | - | - | - | - | - | - | - |
| 92 | 251 cycles | 276,640,240× | 267,780,896× | 286,263,971× | 8,163,993× | 127,489,512× | 86,279,773× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 93 | 506 cycles | 81,160,831× | 81,700,037× | 179,544,564× | 155,902,087× | 86,459,141× | 144,315,659× | - | - | 167,026,085× | 75,182,966× | 100,848,028× | - | - | 48,389,851× | - | - | - | - | - | - | - | - | - | - | - |
| 94 | 266 cycles | 311,602,183× | 301,181,011× | 338,722,661× | 14,699,891× | 134,044,718× | 91,801,929× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 95 | 534 cycles | 89,290,884× | 87,880,629× | 197,665,922× | 170,157,347× | 112,087,707× | 156,075,959× | - | - | 200,623,754× | 83,850,698× | 118,495,416× | - | - | 51,211,597× | - | - | - | - | - | - | - | - | - | - | - |
| 96 | 280 cycles | 343,959,561× | 323,997,946× | 362,173,578× | 47,421,276× | 153,861,817× | 115,134,480× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 97 | 565 cycles | 98,737,235× | 98,659,960× | 216,036,488× | 186,317,161× | 131,500,286× | 176,051,289× | - | - | 217,236,305× | 105,345,540× | 125,125,448× | - | - | 74,830,616× | - | - | - | - | - | - | - | - | - | - | - |
| 98 | 294 cycles | 387,156,014× | 404,466,293× | 402,242,862× | 35,557,367× | 164,203,689× | 123,755,348× | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 99 | 591 cycles | 109,168,440× | 105,419,610× | 236,473,923× | 203,015,028× | 171,680,184× | 190,012,091× | - | - | 248,871,027× | 111,439,588× | 149,417,304× | - | - | 83,846,898× | - | - | - | - | - | - | - | - | - | - | - |
| 100 | 315 cycles | 429,915,921× | 391,255,460× | 454,163,415× | 47,378,062× | 205,117,125× | 145,826,410× | - | - | - | - | 32,248,346× | - | - | - | - | - | - | - | - | - | - | - | - | - | - |