Base 52: Iteration Frequencies: Cycle Start

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
Cycle Start		0.98 step
avg		1.46 step
avg		11.38 step
avg		4.61 step
avg		11.37 step
avg		30.41 step
avg		10.79 step
avg		93.09 step
avg		23.13 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
51×
0s:
1s:
2s:
14×
714×
650×
0s:
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27s:
1×
753×
700×
1,398×
1,390×
1,378×
1,362×
1,342×
1,318×
1,290×
1,258×
1,222×
1,182×
1,138×
1,090×
1,038×
982×
922×
858×
790×
718×
642×
562×
478×
390×
298×
202×
102×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
1×
4,811×
10,860×
43,680×
174,720×
24,960×
22,151×
41,396×
5,906×
4,588×
7,982×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
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23s:
1×
42,557×
47,544×
37,570×
87,400×
108,992×
163,664×
203,314×
253,070×
289,960×
311,784×
334,452×
370,062×
370,032×
291,856×
305,558×
183,552×
174,558×
104,272×
75,270×
45,140×
16,550×
2,070×
588×
0s:
1s:
2s:
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80s:
81s:
82s:
83s:
84s:
1×
223,460×
578,249×
489,324×
457,608×
677,871×
838,547×
703,922×
833,097×
706,002×
632,825×
593,903×
504,802×
553,538×
608,623×
632,339×
676,546×
652,267×
668,264×
669,014×
663,661×
626,763×
757,984×
761,712×
761,498×
707,896×
596,271×
692,299×
746,159×
787,645×
780,654×
831,148×
669,154×
799,437×
716,644×
804,214×
691,184×
664,082×
588,730×
653,139×
671,214×
596,134×
519,199×
525,306×
367,692×
434,680×
351,567×
417,670×
317,013×
364,554×
345,348×
334,298×
263,667×
277,617×
270,083×
178,891×
214,992×
217,537×
208,361×
152,336×
145,515×
139,978×
137,894×
162,388×
179,355×
232,392×
223,053×
177,292×
158,707×
196,506×
167,449×
147,757×
129,565×
122,682×
117,692×
118,347×
120,012×
85,442×
92,143×
93,706×
84,811×
65,466×
64,586×
32,605×
64,274×
0s:
1s:
2s:
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17s:
18s:
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22s:
23s:
1×
699,919×
1,862,818×
3,866,462×
6,118,194×
9,508,702×
13,066,376×
17,860,472×
23,451,700×
28,161,564×
30,218,574×
31,176,712×
35,464,734×
32,291,180×
26,255,046×
18,071,756×
11,453,886×
5,964,062×
3,039,102×
1,278,134×
537,616×
293,838×
31,890×
1,350×
0s:
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327s:
328s:
329s:
330s:
331s:
332s:
333s:
334s:
335s:
336s:
337s:
1×
3,014,581×
13,956,247×
15,376,613×
17,506,026×
17,778,066×
15,675,723×
17,057,071×
18,959,922×
19,320,957×
18,492,366×
16,336,977×
17,997,541×
15,163,498×
14,836,123×
15,201,264×
15,434,295×
18,210,004×
19,146,493×
19,207,374×
20,246,965×
19,530,306×
17,633,015×
16,064,935×
15,676,495×
17,183,891×
19,389,275×
19,911,806×
21,237,102×
20,700,076×
18,409,455×
18,319,599×
19,839,178×
19,450,870×
18,294,849×
17,042,524×
15,613,326×
15,596,538×
16,605,515×
15,737,460×
15,448,984×
15,581,079×
15,703,023×
15,626,340×
17,474,558×
18,641,657×
17,174,185×
14,835,547×
13,652,642×
12,881,021×
13,739,870×
14,786,089×
15,068,633×
15,046,415×
14,761,633×
14,644,532×
14,034,768×
16,078,498×
18,855,901×
17,436,117×
15,829,973×
15,100,718×
16,535,516×
16,551,051×
15,450,516×
13,064,597×
12,948,108×
14,129,836×
13,868,281×
14,048,234×
12,431,939×
11,440,018×
10,811,843×
10,340,850×
11,754,841×
11,633,966×
11,358,797×
10,568,345×
10,096,019×
11,672,797×
10,914,847×
10,372,515×
10,356,254×
11,420,650×
10,543,820×
9,941,294×
9,923,992×
10,597,487×
10,105,997×
9,081,792×
9,518,316×
9,714,890×
9,491,610×
9,133,190×
8,895,400×
8,075,641×
8,373,135×
8,055,475×
8,180,252×
8,993,965×
9,667,571×
9,590,330×
9,251,226×
10,477,647×
10,303,719×
8,993,052×
10,186,908×
10,089,975×
8,848,083×
7,733,132×
6,552,759×
6,072,075×
7,033,835×
7,918,444×
7,776,554×
7,947,278×
7,020,163×
6,022,868×
5,112,215×
5,467,382×
5,124,418×
5,115,178×
5,062,953×
3,863,850×
4,460,423×
4,304,600×
3,995,882×
4,190,546×
4,039,037×
4,215,053×
4,310,583×
4,725,439×
4,731,983×
4,480,824×
5,350,354×
5,911,025×
5,185,095×
5,061,924×
5,372,246×
5,891,870×
5,931,826×
5,328,405×
4,563,222×
4,574,230×
4,076,998×
3,841,665×
3,869,756×
3,230,668×
2,766,943×
3,047,295×
3,787,251×
3,769,137×
3,428,847×
3,587,610×
3,378,389×
2,850,725×
2,916,844×
2,511,302×
2,858,994×
2,404,097×
2,942,494×
2,429,973×
2,547,991×
3,444,778×
3,425,183×
2,815,511×
2,194,387×
2,081,985×
2,536,529×
2,306,053×
2,401,508×
2,754,829×
2,805,115×
3,390,050×
3,464,925×
4,253,125×
5,055,740×
5,649,318×
6,808,079×
6,726,786×
5,966,611×
5,435,554×
4,928,016×
4,816,102×
5,142,024×
4,969,978×
4,006,342×
4,296,411×
3,406,064×
3,556,247×
3,839,886×
4,096,553×
3,744,241×
3,646,878×
4,093,818×
4,091,892×
3,318,838×
2,208,688×
2,635,260×
2,833,403×
3,612,700×
2,900,173×
3,190,430×
3,329,742×
3,927,893×
3,816,438×
4,368,446×
5,136,812×
4,814,058×
4,943,693×
4,844,856×
4,425,366×
4,749,250×
5,406,908×
4,932,376×
6,288,718×
6,476,056×
6,991,573×
5,679,124×
5,894,553×
5,702,035×
5,362,871×
4,725,619×
4,036,205×
4,598,220×
3,752,042×
4,099,783×
4,012,883×
3,638,115×
2,808,821×
2,852,720×
2,212,065×
2,053,893×
1,325,889×
1,224,635×
1,150,033×
1,114,169×
798,083×
655,357×
657,110×
1,062,881×
1,853,902×
1,340,874×
1,704,357×
1,661,518×
2,124,904×
2,303,517×
2,482,410×
2,330,692×
2,438,376×
2,240,114×
2,161,833×
1,708,903×
1,844,644×
2,063,189×
2,522,422×
2,159,232×
1,966,093×
1,421,154×
1,458,962×
1,344,432×
1,520,335×
1,989,436×
2,336,720×
3,239,894×
3,342,848×
3,991,634×
3,723,568×
3,309,141×
2,959,795×
2,750,397×
2,467,245×
2,697,750×
2,625,433×
2,004,630×
2,195,611×
2,538,639×
2,925,143×
3,028,602×
2,622,136×
1,736,631×
1,909,946×
2,301,307×
1,866,853×
1,958,745×
2,152,074×
2,369,556×
2,948,331×
2,228,866×
1,968,323×
1,915,546×
1,634,286×
1,674,594×
1,529,243×
2,015,848×
1,861,934×
1,924,496×
932,567×
630,592×
463,760×
552,658×
762,561×
746,853×
780,566×
814,388×
872,704×
1,055,544×
1,178,694×
711,802×
960,617×
497,435×
628,056×
1,055,433×
1,370,441×
899,407×
713,863×
553,049×
931,877×
688,723×
350,556×
433,901×
474,474×
743,728×
689,586×
582,184×
313,963×
266,482×
298,634×
319,467×
251,210×
303,852×
229,944×
93,454×
88,174×
16,300×
7,984×
26,865×
6,944×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
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45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
1×
5,170,171×
24,384,108×
59,446,374×
122,530,476×
194,134,494×
291,656,512×
436,927,378×
490,627,468×
638,058,816×
662,091,980×
618,604,124×
583,581,660×
506,455,374×
503,439,352×
487,919,908×
454,672,570×
449,797,282×
412,842,278×
331,784,488×
263,273,804×
221,059,444×
166,966,148×
206,538,802×
195,148,574×
227,376,546×
220,805,242×
227,264,884×
208,879,726×
231,766,798×
217,150,614×
180,183,568×
216,013,838×
204,397,036×
339,829,592×
358,763,142×
478,132,334×
509,574,126×
504,197,254×
470,977,674×
400,630,752×
375,748,186×
346,376,458×
271,190,124×
163,114,986×
99,912,030×
57,895,364×
43,830,566×
29,480,550×
31,705,500×
24,349,782×
12,087,504×
4,000,278×
388,778×
7,842×