| 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 | 0.97 step avg | 1.43 step avg | 7.21 step avg | 3.27 step avg | 9.85 step avg | 18.76 step avg | 12.54 step avg | 46.37 step avg | 14.46 step avg | 32.85 step avg | 19.74 step avg | 43.73 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 29× | 0s: 1s: 2s: 9× 246× 210× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 1× 269× 238× 474× 466× 454× 438× 418× 394× 366× 334× 298× 258× 214× 166× 114× 58× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 2,269× 5,334× 21,420× 5,374× 4,627× 1,143× 752× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 1× 1,927× 2,524× 3,370× 7,482× 14,552× 21,366× 22,268× 24,416× 23,914× 28,896× 34,308× 27,640× 22,334× 19,774× 15,156× 6,756× 1,572× | 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: 1× 36,113× 92,207× 76,823× 49,228× 57,939× 71,090× 72,023× 77,228× 76,450× 82,004× 66,956× 52,113× 45,264× 37,952× 30,817× 29,747× 21,075× 18,091× 17,310× 18,774× 23,261× 17,153× 18,973× 20,103× 30,363× 25,219× 28,433× 30,803× 22,851× 19,991× 15,512× 11,873× 11,167× 15,736× 14,698× 12,796× 10,774× 8,083× 10,549× 12,612× 17,124× 17,115× 22,340× 18,148× 10,974× 11,610× 13,790× 16,380× 8,992× 11,957× 11,663× 17,425× 21,070× 15,594× 7,052× 6,614× 3,802× 1,355× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 1× 17,509× 41,294× 72,922× 98,992× 173,234× 169,978× 269,264× 326,456× 459,164× 540,102× 597,250× 778,736× 973,644× 1,151,094× 985,404× 754,212× 540,198× 265,112× 93,918× 34,788× 4,408× | 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: 1× 38,661× 219,098× 278,983× 262,730× 388,704× 577,106× 695,929× 667,593× 580,714× 573,537× 794,608× 763,227× 787,497× 548,151× 565,247× 609,631× 683,382× 598,684× 511,431× 440,928× 559,879× 566,424× 518,567× 454,183× 552,448× 515,778× 487,568× 491,816× 552,902× 481,598× 523,624× 412,532× 429,378× 295,116× 355,952× 442,731× 324,557× 374,982× 500,228× 417,380× 417,372× 412,416× 344,889× 303,190× 385,922× 413,435× 429,356× 288,454× 303,231× 329,741× 357,801× 420,917× 407,047× 371,763× 350,275× 313,690× 297,445× 283,816× 291,011× 352,246× 374,059× 352,040× 312,361× 228,024× 187,878× 188,950× 173,092× 188,476× 225,942× 262,793× 195,335× 226,714× 209,887× 206,873× 213,944× 162,735× 167,296× 119,085× 132,624× 116,095× 120,318× 161,313× 226,985× 245,537× 302,614× 205,673× 164,041× 190,367× 182,208× 200,760× 242,184× 195,765× 153,790× 118,896× 163,557× 197,833× 210,777× 217,797× 191,610× 176,094× 229,386× 244,878× 240,959× 226,228× 160,951× 184,428× 258,118× 252,268× 209,142× 203,302× 152,705× 126,581× 119,853× 127,383× 103,747× 113,923× 131,971× 126,523× 76,064× 36,294× 25,473× 26,012× 33,078× 44,762× 45,016× 23,555× 16,620× 12,676× 9,591× 10,445× 2,586× 3,284× 394× | 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: 1× 92,255× 406,832× 1,067,156× 2,035,240× 4,201,806× 5,883,292× 7,391,962× 8,299,516× 7,296,206× 6,927,306× 9,726,066× 13,178,576× 15,111,462× 14,638,912× 13,664,930× 11,497,006× 6,429,834× 4,210,428× 3,206,754× 2,673,912× 2,210,908× 1,764,750× 1,340,368× 1,307,658× 2,258,458× 2,306,238× 3,093,286× 2,579,618× 1,861,014× 998,940× 753,472× 1,328,724× 1,102,288× 1,451,882× 608,766× 105,818× | 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: 1× 421,878× 4,743,968× 9,088,509× 9,270,831× 12,578,887× 16,748,197× 18,508,166× 17,621,800× 15,612,335× 13,565,188× 13,501,353× 14,315,605× 15,472,375× 16,238,642× 16,319,235× 14,009,159× 13,430,329× 14,007,166× 13,199,314× 10,617,447× 11,082,969× 11,049,549× 9,925,568× 10,379,388× 10,378,655× 8,978,556× 7,430,185× 6,859,039× 6,499,068× 6,287,627× 6,102,989× 5,672,923× 4,500,116× 3,521,701× 2,696,348× 2,896,401× 2,935,284× 3,496,969× 4,804,048× 5,820,183× 5,411,144× 5,525,863× 5,662,809× 7,190,050× 6,772,090× 9,053,773× 8,294,436× 7,809,185× 8,398,688× 7,504,379× 6,935,998× 7,661,510× 9,950,921× 12,738,850× 10,728,023× 9,171,344× 6,792,758× 7,663,266× 8,283,824× 7,149,230× 5,791,236× 5,617,016× 5,804,165× 4,661,985× 4,403,198× 4,335,059× 4,915,248× 6,032,507× 4,912,091× 4,203,563× 3,077,103× 3,267,850× 3,292,281× 2,905,004× 2,619,445× 2,133,396× 1,742,900× 1,388,684× 1,200,706× 1,908,738× 1,755,936× 2,135,128× 1,528,334× 1,372,847× 1,032,755× 847,526× 495,328× 504,935× 598,302× 408,708× 188,393× 114,999× 134,969× 188,747× 188,290× 133,250× 139,229× 115,861× 92,627× 75,032× 66,997× 33,844× 45,260× 13,520× 2,680× 19,232× 14,400× | 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: 1× 972,755× 6,878,818× 20,489,810× 36,501,926× 53,273,408× 76,692,368× 91,375,710× 110,092,414× 107,686,306× 98,140,816× 90,111,022× 89,552,942× 73,302,766× 62,946,968× 50,591,290× 51,540,652× 53,436,238× 58,292,788× 73,423,998× 81,942,920× 82,359,028× 71,482,110× 61,267,700× 55,012,412× 45,572,142× 41,392,952× 42,684,948× 49,514,850× 56,736,818× 55,324,752× 48,415,654× 42,536,006× 45,452,468× 61,675,946× 48,848,912× 33,956,568× 28,753,262× 28,649,526× 29,096,606× 33,845,156× 23,752,550× 15,939,172× 11,173,496× 5,939,034× 3,627,754× 1,388,516× 143,266× 13,920× | 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: 1× 1,077,837× 21,813,908× 47,588,715× 53,012,511× 69,045,793× 89,903,189× 93,546,919× 91,515,683× 77,520,297× 77,345,367× 77,729,584× 72,186,676× 88,661,929× 87,488,916× 79,686,988× 72,354,948× 72,438,283× 70,337,687× 84,829,755× 88,283,976× 92,544,608× 78,652,404× 73,300,209× 80,218,354× 97,011,054× 128,644,951× 145,790,463× 144,570,928× 130,981,304× 126,294,898× 123,727,544× 121,554,348× 126,737,036× 123,525,590× 133,669,674× 141,559,198× 156,090,402× 132,255,787× 125,604,299× 117,067,350× 137,861,289× 135,833,254× 126,879,063× 116,132,901× 102,200,483× 90,163,007× 92,442,497× 96,811,209× 97,235,289× 99,584,661× 94,712,474× 90,519,628× 82,330,654× 87,867,579× 83,840,017× 85,781,966× 93,537,868× 100,937,940× 100,554,355× 104,232,643× 91,722,374× 88,732,480× 91,489,869× 95,178,109× 100,332,787× 111,372,053× 94,932,556× 87,252,599× 78,280,203× 70,084,959× 71,402,119× 74,006,566× 79,427,521× 73,570,187× 65,506,394× 59,934,096× 51,835,932× 60,682,070× 56,352,283× 50,662,491× 50,664,530× 49,209,304× 41,234,964× 36,237,377× 35,190,775× 27,929,923× 24,289,123× 26,034,802× 23,020,752× 19,410,935× 19,524,108× 16,364,772× 16,180,048× 17,916,606× 14,513,295× 9,376,481× 9,135,022× 10,493,216× 9,307,291× 7,280,120× 5,578,245× 5,135,515× 6,315,999× 7,644,241× 5,442,080× 2,934,569× 2,650,405× 1,797,449× 1,695,834× 1,633,991× 1,646,678× 718,381× 404,655× 210,446× 252,141× 121,873× 268,078× 470,716× 485,423× 452,558× 508,678× 144,869× 153,814× 226,200× 49,150× 13,700× |