Base 50: Iteration Frequencies: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ

Color Key
OrangeFixed Pointnumber that becomes itself after one iteration
GreenFinal Numbersall numbers eventually reached, from all cycles
PurpleCycle Startiterations include entry into cycle, assuming it repeats
RedFull Cycleiterations include entire cycle, proving it repeats
BlueStart Numberssubset (optimization) of all numbers; minimal for full coverage
GrayNo Resultsany calculation that has no results

Digits 1 2 3 4 5 6 7 8 9
Average Steps
Full Cycle
1.98 step
avg
7.69 step
avg
12.00 step
avg
12.50 step
avg
15.05 step
avg
72.56 step
avg
19.73 step
avg
438.89 step
avg
33.67 step
avg
Step Frequency
Full Cycle
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49×
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81×
16×

204×
184×


376×
400×
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699×
648×
1,294×
1,286×
1,274×
1,258×
1,238×
1,214×
1,186×
1,154×
1,118×
1,078×
1,034×
986×
934×
878×
818×
754×
686×
614×
538×
458×
374×
286×
194×
98×
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469×
650×
2,700×

1,140×
3,394×
13,500×
2,349×
1,672×
16,349×
41,608×
162,000×
23,270×
20,301×
2,284×
1,138×
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49×
1,898×
650×
20,740×
28,278×
33,680×
77,296×
104,690×
166,780×
202,326×
252,258×
259,446×
343,726×
269,648×
287,758×
241,094×
215,708×
188,686×
141,154×
111,244×
72,244×
56,162×
41,534×
28,518×
15,648×
1,294×
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699×
5,004×
17,772×
63,724×
140,783×
55,741×
52,587×
74,698×
56,853×
61,929×
42,120×
32,132×
24,942×
15,416×
12,912×
9,989×
8,758×
6,048×
16,104×
12,534×
10,978×
7,240×
6,868×
38,359×
96,067×
77,650×
72,002×
88,440×
105,182×
119,758×
89,003×
98,294×
118,132×
168,653×
178,315×
233,474×
211,278×
236,907×
261,037×
268,860×
236,339×
237,526×
336,832×
332,973×
328,685×
326,801×
309,199×
361,839×
309,961×
385,986×
523,350×
515,110×
546,514×
528,816×
585,991×
438,248×
476,231×
466,561×
458,683×
559,733×
605,711×
611,949×
597,832×
491,776×
468,528×
536,607×
526,137×
500,034×
368,786×
376,485×
382,111×
317,562×
268,593×
243,989×
224,061×
155,774×
215,320×
209,885×
204,128×
173,862×
189,509×
242,646×
237,134×
239,136×
231,291×
236,612×
198,944×
221,617×
193,073×
164,133×
185,001×
196,420×
258,672×
253,900×
246,093×
211,157×
206,599×
183,440×
247,659×
198,364×
247,679×
192,538×
215,258×
274,789×
219,924×
239,562×
305,546×
238,117×
258,400×
320,553×
302,106×
193,647×
176,856×
207,057×
153,052×
167,502×
178,797×
160,854×
98,259×
98,670×
107,508×
84,680×
87,514×
107,705×
96,219×
75,419×
84,685×
47,876×
58,411×
59,603×
89,145×
80,241×
130,850×
83,590×
81,109×
59,051×
40,277×
26,680×
22,630×
14,051×
8,154×
11,960×
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49×


120,510×
322,714×
713,038×
939,988×
1,338,738×
2,089,288×
3,154,228×
4,897,644×
7,077,386×
8,721,462×
10,606,880×
11,773,498×
14,295,026×
16,676,826×
19,558,430×
21,309,680×
23,802,224×
21,548,856×
19,630,026×
15,570,212×
11,103,902×
6,223,870×
4,304,386×
2,970,620×
1,724,340×
844,744×
585,834×
13,000×
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49×

16,368×
64,816×
55,124×
238,190×
390,166×
620,659×
955,595×
949,171×
1,123,196×
1,147,485×
1,620,997×
926,033×
763,173×
369,153×
386,789×
450,274×
540,626×
273,090×
244,881×
207,277×
175,233×
152,955×
205,654×
233,546×
115,491×
131,961×
155,902×
108,734×
203,580×
225,126×
393,804×
252,778×
183,846×
68,173×
94,036×
97,892×
111,324×
119,246×
85,327×
110,912×
68,688×
153,177×
133,181×
203,928×
64,258×
31,914×
41,278×
10,720×










































































































































































































































































































2,340,813×
11,732,029×
11,982,397×
12,447,761×
12,679,428×
11,121,244×
10,204,095×
10,107,351×
11,451,649×
12,651,741×
13,314,959×
13,082,113×
11,989,266×
10,487,989×
12,532,666×
10,568,280×
10,622,902×
10,581,667×
11,515,440×
11,605,522×
10,820,863×
10,338,448×
10,515,633×
11,689,166×
11,077,617×
10,643,297×
10,768,550×
11,482,209×
9,944,961×
9,545,133×
10,591,687×
11,831,564×
12,762,278×
11,709,421×
10,953,976×
9,948,506×
9,770,722×
10,372,798×
10,437,997×
10,009,046×
9,582,507×
9,233,506×
8,528,841×
8,304,540×
9,348,829×
9,683,633×
10,034,900×
9,035,472×
8,721,653×
8,801,447×
9,784,830×
9,800,887×
9,541,719×
9,205,316×
9,333,702×
9,894,692×
11,403,894×
10,172,613×
8,937,189×
8,907,172×
9,155,877×
9,104,430×
8,960,065×
9,214,801×
9,776,492×
10,381,636×
9,733,517×
9,723,042×
10,071,794×
9,037,827×
9,190,177×
9,704,508×
10,562,694×
9,425,415×
8,769,861×
7,602,334×
8,084,656×
8,292,925×
9,558,152×
11,795,017×
10,303,907×
9,746,973×
9,869,871×
8,575,282×
8,429,437×
9,667,003×
10,782,811×
9,582,214×
9,134,054×
9,705,703×
9,794,952×
9,066,134×
9,648,879×
8,958,284×
8,370,819×
6,960,593×
7,035,496×
7,356,985×
8,064,398×
7,486,025×
7,851,077×
8,068,390×
8,018,437×
7,519,418×
7,235,997×
6,864,248×
6,362,753×
7,274,826×
7,350,426×
7,036,483×
6,149,411×
6,135,737×
6,233,563×
6,786,675×
6,321,337×
6,230,002×
6,172,984×
4,975,762×
4,641,506×
4,115,706×
4,434,838×
4,253,616×
3,955,380×
4,397,093×
5,164,623×
5,913,275×
4,848,080×
3,921,221×
4,396,035×
4,703,779×
4,874,597×
4,972,508×
4,209,810×
4,571,271×
4,689,165×
4,512,283×
4,293,447×
3,860,838×
3,240,008×
3,487,819×
3,935,811×
3,676,103×
3,225,019×
3,228,290×
4,084,751×
3,018,610×
2,916,829×
3,090,048×
3,809,769×
3,804,105×
3,275,469×
3,385,829×
3,915,152×
3,995,335×
3,624,117×
3,518,943×
3,302,317×
3,766,951×
3,638,393×
3,851,315×
5,346,542×
6,762,322×
7,238,356×
7,353,083×
7,054,982×
5,602,551×
4,710,828×
3,741,246×
3,752,547×
4,317,074×
4,763,407×
4,661,544×
3,642,778×
3,814,231×
4,435,842×
4,092,876×
4,505,830×
4,301,208×
4,494,070×
3,961,808×
3,926,429×
4,654,046×
4,513,792×
4,693,617×
4,774,998×
5,865,772×
7,121,243×
7,635,339×
7,781,152×
7,091,025×
5,832,220×
5,641,315×
7,119,838×
6,828,661×
6,634,656×
6,100,772×
5,808,390×
5,180,224×
4,942,900×
4,066,705×
4,565,343×
5,392,664×
5,326,435×
4,749,315×
4,686,231×
4,591,603×
3,770,782×
3,121,781×
3,593,669×
4,243,712×
4,278,010×
4,775,119×
3,732,131×
3,752,079×
4,040,595×
3,874,404×
4,374,507×
3,867,942×
3,780,160×
2,658,866×
2,839,429×
3,172,972×
3,129,143×
3,643,597×
4,034,763×
4,278,812×
3,034,917×
2,785,773×
2,285,277×
1,842,259×
1,320,209×
1,454,702×
1,791,171×
2,267,141×
1,582,715×
1,268,814×
1,054,882×
697,107×
571,967×
617,970×
503,001×
564,660×
607,607×
663,192×
677,305×
780,439×
692,575×
696,015×
554,492×
581,126×
588,058×
504,431×
299,330×
429,645×
130,496×
84,746×
175,278×
546,132×
648,307×
812,139×
592,862×
105,529×
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282,109×
1,793,218×
5,879,098×
12,571,326×
26,144,854×
41,794,150×
73,097,196×
98,846,928×
108,758,564×
134,423,076×
143,920,204×
177,614,456×
173,837,494×
226,568,406×
219,031,874×
235,942,032×
205,349,592×
154,551,284×
112,011,418×
56,740,650×
21,703,772×
25,396,902×
39,186,024×
81,059,240×
143,862,628×
195,928,900×
286,688,864×
317,540,478×
366,902,030×
375,981,346×
386,429,644×
402,128,908×
423,690,036×
446,292,488×
438,096,822×
383,789,980×
324,393,798×
337,694,122×
282,533,234×
280,808,376×
291,615,666×
290,666,678×
246,386,698×
217,781,542×
202,585,210×
188,607,660×
160,590,438×
138,410,532×
168,131,418×
179,051,250×
158,800,660×
128,482,204×
115,524,290×
92,136,398×
68,331,832×
65,575,674×
41,857,298×
35,573,674×
25,085,832×
18,636,204×
7,242,358×
6,320,786×
6,106,006×
9,783,550×
12,440,702×
3,485,736×
377,412×
20,720×