Base 28: Iteration Frequencies: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV

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 10 11 12
Average Steps
Full Cycle
1.96 step
avg
14.53 step
avg
7.83 step
avg
9.15 step
avg
10.22 step
avg
45.29 step
avg
23.72 step
avg
50.25 step
avg
22.98 step
avg
136.51 step
avg
39.61 step
avg
96.49 step
avg
Step Frequency
Full Cycle
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27×
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27×












189×
182×
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237×
208×
414×
406×
394×
378×
358×
334×
306×
274×
238×
198×
154×
106×
54×
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27×

352×
660×
2,688×
10,752×
3,128×
2,903×
5,394×
760×
268×
526×
640×
324×
568×
432×
738×
1,304×
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27×
600×
3,096×
8,374×
9,616×
12,984×
17,878×
20,858×
29,922×
29,136×
27,296×
18,904×
13,304×
7,196×
2,184×
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237×

1,088×
3,278×
2,608×
2,848×
3,254×
3,722×
9,338×
12,123×
11,946×
13,510×
11,844×
15,075×
15,366×
12,602×
8,996×
9,840×
12,364×
5,613×
6,902×
7,322×
5,269×
2,884×
2,644×




10,178×
20,650×
26,008×
29,259×
26,804×
31,821×
24,413×
31,102×
38,847×
31,704×
25,046×
25,674×
16,339×
20,775×
19,768×
20,434×
19,758×
15,563×
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×
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3,611×
13,320×
26,546×
58,372×
66,366×
84,754×
131,736×
160,430×
91,180×
21,398×
13,704×
4,092×
1,140×





63,896×
142,034×
238,114×
384,398×
532,530×
589,210×
659,922×
679,242×
625,692×
448,582×
198,038×
85,904×
36,020×
17,646×
1,738×
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1,307×
2,230×
4,660×
24,928×
18,484×
19,259×
27,089×
44,216×
61,095×
57,709×
57,910×
96,620×
116,902×
132,256×
108,832×
128,569×
151,030×
138,661×
166,616×
176,419×
212,640×
229,195×
221,870×
225,582×
230,408×
239,370×
200,123×
161,371×
169,715×
165,060×
208,550×
372,322×
394,755×
362,482×
503,915×
559,317×
635,200×
576,935×
550,051×
604,954×
696,031×
718,604×
705,806×
777,510×
814,946×
709,406×
623,053×
510,805×
466,519×
452,279×
554,514×
433,582×
327,547×
274,316×
273,349×
268,297×
306,187×
258,368×
180,042×
189,356×
199,857×
203,644×
174,133×
238,494×
195,740×
194,746×
208,757×
181,837×
203,367×
184,024×
225,947×
148,927×
166,053×
158,106×
163,604×
169,542×
188,504×
145,230×
111,718×
96,399×
77,050×
114,446×
131,631×
111,295×
86,937×
91,639×
95,317×
76,698×
64,648×
59,732×
60,722×
55,767×
60,332×
52,142×
42,579×
23,448×
13,377×
7,078×
8,494×
12,940×
29,674×
39,791×
52,348×
47,856×
28,302×
12,476×
23,552×
32,384×
26,700×
35,832×
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×
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9,957×
48,920×
133,050×
113,022×
300,958×
233,118×
321,250×
85,706×
8,448×
98,072×
412,152×
1,092,190×
2,089,154×
3,770,056×
5,401,910×
6,122,102×
6,409,916×
6,030,424×
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×
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1,947×
6,130×
17,308×
208,000×
323,307×
316,461×
466,379×
567,751×
451,041×
434,769×
492,014×
661,092×
855,841×
646,252×
698,723×
836,945×
989,457×
846,959×
744,509×
522,698×
465,462×
557,085×
476,883×
501,373×
361,632×
287,049×
470,358×
585,567×
935,032×
1,102,495×
1,014,217×
1,037,077×
816,621×
669,717×
558,261×
705,338×
799,799×
573,976×
650,271×
579,816×
524,566×
536,594×
477,461×
319,541×
372,097×
386,305×
427,950×
345,913×
288,833×
305,444×
504,607×
412,149×
477,536×
235,655×
271,808×
610,617×
580,050×
536,698×
332,407×
218,658×
147,697×
210,990×
338,652×
314,108×
234,180×
214,192×
261,038×
198,086×
142,986×
216,037×
289,702×
386,697×
327,779×
456,556×
408,015×
171,502×
118,822×
80,693×
208,361×
319,521×
383,982×
491,505×
511,635×
442,202×
189,399×
95,328×
30,190×
21,303×
3,122×
432×




















275,701×
2,451,400×
4,017,013×
3,628,461×
3,750,252×
4,182,176×
5,325,102×
4,978,638×
4,576,537×
4,928,433×
4,153,318×
4,693,917×
5,416,052×
5,424,926×
5,324,253×
5,334,632×
5,569,014×
6,143,026×
6,094,839×
5,534,524×
4,797,203×
4,120,470×
4,311,806×
4,587,802×
5,003,581×
4,591,517×
4,035,553×
3,738,692×
4,105,103×
4,078,200×
4,253,433×
4,190,368×
4,816,592×
4,452,794×
4,610,216×
4,574,994×
4,247,019×
4,245,854×
4,778,071×
3,948,149×
3,988,843×
4,152,722×
4,171,468×
5,115,757×
5,036,152×
4,589,204×
4,397,341×
3,965,369×
3,797,869×
4,042,516×
3,642,302×
4,004,137×
3,259,305×
2,912,129×
2,816,082×
3,000,609×
3,394,798×
2,950,987×
2,772,900×
2,885,671×
2,727,607×
2,230,799×
2,327,719×
2,327,354×
2,540,816×
2,083,961×
1,530,429×
1,477,452×
1,803,337×
2,202,642×
2,525,653×
2,489,537×
2,591,206×
1,934,854×
1,559,728×
1,434,674×
1,466,136×
1,860,307×
1,453,060×
1,821,968×
1,247,980×
1,166,065×
983,562×
1,134,173×
966,298×
1,006,423×
1,116,254×
901,109×
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×
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27,027×
206,010×
892,190×
2,094,996×
5,003,738×
9,336,544×
13,305,024×
17,845,326×
13,082,944×
9,718,574×
7,558,182×
7,514,706×
11,279,546×
9,536,440×
9,607,282×
9,610,198×
12,598,246×
10,880,714×
13,634,808×
15,931,886×
25,586,556×
34,812,388×
48,022,854×
53,979,776×
48,848,458×
38,401,814×
31,698,416×
28,860,676×
20,893,488×
16,402,588×
12,407,970×
10,776,296×
13,142,724×
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×
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2,157×
9,970×
86,224×
2,202,468×
4,828,213×
4,099,711×
6,663,833×
6,994,074×
5,321,696×
7,808,319×
9,910,268×
9,781,859×
8,092,878×
6,939,948×
8,155,666×
10,473,200×
14,464,254×
15,478,334×
12,390,469×
12,200,149×
12,746,290×
14,983,102×
14,648,942×
14,945,118×
12,539,304×
12,965,397×
17,747,642×
21,590,805×
17,184,798×
17,306,961×
15,035,051×
16,388,935×
21,309,827×
22,006,938×
22,003,401×
16,988,700×
17,006,185×
19,271,728×
25,633,316×
33,565,393×
36,553,035×
30,984,997×
34,378,119×
44,754,044×
51,717,607×
45,510,643×
43,481,391×
45,446,317×
45,853,349×
52,793,767×
54,506,903×
48,573,636×
43,311,191×
43,259,061×
49,466,328×
58,016,556×
51,286,964×
50,264,792×
40,782,541×
33,697,606×
36,442,783×
39,416,607×
42,479,210×
40,341,325×
44,574,959×
42,985,203×
37,400,205×
41,821,502×
39,895,169×
37,371,854×
40,645,281×
38,514,462×
43,763,639×
44,741,252×
41,757,774×
40,318,027×
39,116,117×
33,701,683×
31,927,317×
27,168,248×
26,086,565×
24,882,850×
28,610,918×
26,052,579×
24,339,145×
18,718,624×
17,108,038×
15,966,032×
16,321,818×
18,136,035×
20,706,461×
20,980,444×
17,768,033×
17,264,293×
15,171,451×
13,698,019×
10,182,037×
9,061,539×
10,316,565×
11,550,426×
10,934,724×
8,466,099×
8,794,027×
9,292,243×
9,647,330×
9,757,207×
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5,439,206×
5,892,100×
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5,696,201×
5,859,424×
7,521,684×
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7,157,760×
8,503,400×
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6,820,898×
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13,957,721×
11,576,160×
10,644,058×
10,488,848×
9,231,111×
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6,642,775×
3,893,897×
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3,663,805×
5,133,818×
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860,546×
353,448×
246,989×
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21,142×