Base 52: 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		26.52 step
avg		12.38 step
avg		10.04 step
avg		14.70 step
avg		135.10 step
avg		27.04 step
avg		210.63 step
avg		27.96 step
avg
Step Frequency
Full Cycle
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1s:
2s:
0×
1×
51×
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0×
1×
51×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
13×
663×
650×
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27s:
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0×
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:
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7s:
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9s:
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14s:
15s:
16s:
0×
1×
51×
0×
952×
2,172×
8,736×
38,752×
13,704×
39,578×
147,908×
19,944×
17,517×
33,264×
5,906×
4,588×
7,982×
0s:
1s:
2s:
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0×
1×
51×
2,052×
17,988×
44,358×
40,692×
55,604×
101,718×
129,908×
200,100×
226,720×
294,256×
285,208×
382,372×
346,048×
410,976×
292,134×
330,464×
204,220×
187,484×
122,600×
80,056×
45,496×
16,652×
2,070×
588×
0s:
1s:
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0×
1×
753×
1,743×
5,253×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
37,060×
107,852×
47,614×
41,278×
76,138×
75,356×
86,205×
94,563×
71,525×
74,905×
84,288×
73,776×
73,932×
73,513×
83,664×
62,872×
38,394×
27,303×
29,376×
20,102×
11,016×
9,354×
11,284×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
183,904×
465,144×
441,710×
416,330×
601,733×
763,191×
617,717×
738,534×
634,477×
557,920×
509,615×
431,026×
479,606×
535,110×
548,675×
613,674×
613,873×
640,961×
639,638×
643,559×
615,747×
748,630×
750,428×
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:
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0×
1×
35,723×
132,546×
402,074×
736,582×
1,172,422×
1,335,606×
2,010,480×
2,960,268×
3,989,066×
5,617,606×
5,987,092×
6,886,014×
5,305,094×
3,444,438×
3,160,790×
1,540,160×
671,166×
534,684×
671,012×
1,730,272×
3,464,388×
5,381,612×
8,336,280×
11,730,770×
15,849,992×
20,491,432×
24,172,498×
24,600,968×
25,189,620×
28,578,720×
26,986,086×
22,810,608×
14,910,966×
9,913,726×
5,292,896×
2,504,418×
1,271,318×
537,616×
293,838×
31,890×
1,350×
0s:
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0×
1×
51×
0×
0×
4,350×
18,174×
4,540×
0×
0×
0×
0×
73,444×
491,486×
519,356×
690,634×
945,653×
1,007,732×
1,179,332×
1,036,423×
718,208×
847,252×
852,994×
825,601×
781,488×
733,327×
606,472×
726,779×
686,138×
477,680×
157,047×
75,258×
156,506×
448,395×
509,552×
489,414×
232,783×
146,218×
178,824×
388,792×
1,288,218×
1,647,098×
1,609,762×
1,555,010×
1,201,592×
1,067,477×
1,058,446×
978,709×
1,116,277×
1,063,861×
1,266,885×
1,238,725×
989,905×
984,467×
748,165×
962,991×
1,203,043×
1,088,458×
1,011,272×
918,084×
843,346×
734,252×
694,961×
723,693×
690,380×
510,106×
697,376×
779,463×
1,094,441×
1,253,869×
1,042,594×
1,303,936×
1,745,691×
1,426,648×
1,662,706×
3,466,410×
3,427,746×
3,610,449×
3,900,990×
3,360,483×
3,538,188×
3,191,878×
3,302,384×
3,066,661×
2,960,139×
4,047,604×
3,754,391×
3,519,803×
4,356,835×
4,185,338×
3,891,076×
4,781,511×
4,859,674×
4,839,571×
4,985,652×
5,720,131×
5,755,505×
5,289,511×
5,360,987×
6,533,806×
6,581,711×
7,990,908×
9,090,689×
8,819,395×
8,204,233×
8,198,306×
8,201,278×
8,060,509×
8,101,930×
8,189,420×
8,926,698×
9,402,838×
8,506,736×
6,765,447×
7,384,445×
9,923,848×
10,741,847×
11,730,143×
11,754,901×
12,043,603×
10,990,516×
10,887,794×
10,416,533×
10,237,770×
9,333,220×
10,078,651×
10,759,160×
8,839,391×
9,005,702×
9,706,391×
11,301,080×
11,904,025×
10,971,980×
9,803,416×
8,761,379×
9,605,852×
9,403,955×
8,939,073×
7,145,831×
8,130,612×
10,723,530×
11,386,910×
10,907,902×
8,819,782×
9,554,706×
9,286,254×
8,735,392×
9,009,320×
7,454,211×
6,856,731×
6,507,501×
6,125,848×
7,210,861×
8,315,477×
8,341,101×
9,069,254×
10,529,339×
10,506,910×
10,180,882×
8,798,210×
8,240,628×
7,052,303×
7,098,482×
8,101,910×
8,313,962×
7,509,583×
7,033,729×
7,892,577×
7,383,365×
6,435,421×
6,963,214×
8,022,899×
7,242,576×
6,929,355×
7,371,217×
10,220,069×
15,072,144×
14,577,051×
15,668,248×
15,794,512×
14,364,577×
14,420,617×
16,337,181×
16,374,563×
14,587,289×
15,059,078×
17,410,026×
15,542,499×
15,378,632×
14,680,350×
14,851,694×
17,030,145×
17,859,815×
17,410,607×
18,128,180×
17,408,198×
15,224,876×
14,066,557×
14,113,374×
16,509,359×
17,175,512×
15,861,251×
13,803,996×
11,972,636×
11,235,265×
11,286,007×
12,513,715×
11,301,845×
10,045,857×
10,352,591×
9,271,812×
8,458,551×
9,245,946×
10,192,954×
11,146,182×
10,626,303×
11,767,509×
11,036,952×
10,441,199×
11,114,747×
9,758,104×
8,439,788×
7,754,445×
6,714,197×
8,089,993×
8,423,378×
8,721,765×
8,095,301×
9,443,522×
9,337,690×
7,925,622×
6,919,067×
7,219,293×
7,344,536×
6,408,177×
6,218,284×
5,601,495×
6,109,219×
5,361,066×
4,700,966×
4,600,522×
4,389,475×
4,459,637×
4,485,079×
4,680,325×
3,729,174×
3,438,586×
3,941,512×
3,984,123×
3,522,222×
4,001,424×
3,302,567×
2,815,441×
3,099,092×
2,874,183×
3,104,645×
2,947,900×
2,625,988×
2,504,412×
2,522,109×
1,895,126×
1,660,532×
2,192,468×
2,767,649×
2,566,155×
2,652,053×
2,852,026×
2,742,646×
2,399,340×
2,163,578×
1,782,425×
1,769,656×
1,904,060×
2,432,802×
2,309,596×
2,077,027×
2,278,073×
2,526,104×
2,727,144×
2,417,379×
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3,011,208×
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1,364,198×
1,704,770×
2,245,553×
2,301,783×
2,705,255×
2,690,212×
2,456,725×
2,592,515×
2,612,149×
3,640,692×
3,899,943×
3,197,060×
2,964,672×
3,927,057×
5,298,694×
4,713,896×
4,467,999×
4,290,463×
4,712,510×
4,133,443×
4,240,841×
4,911,318×
4,589,201×
3,579,569×
3,264,447×
3,432,772×
3,806,227×
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2,980,250×
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2,740,405×
3,034,811×
3,959,257×
4,623,680×
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5,343,164×
4,958,546×
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5,865,005×
6,093,260×
5,762,747×
5,628,669×
4,729,906×
4,858,323×
4,905,381×
4,514,798×
4,259,272×
4,463,204×
5,361,998×
4,489,280×
3,776,503×
2,870,913×
3,098,625×
2,874,759×
3,059,907×
3,203,491×
3,587,348×
4,345,093×
4,600,420×
5,489,967×
5,435,505×
5,304,555×
4,740,813×
5,230,350×
5,019,131×
4,811,591×
4,591,865×
4,348,783×
4,622,176×
5,929,060×
6,674,121×
6,891,666×
5,436,634×
4,569,519×
5,151,930×
5,128,465×
4,282,271×
4,135,119×
4,457,199×
4,313,859×
5,067,463×
3,957,563×
3,693,898×
3,085,648×
2,958,881×
2,586,386×
2,419,047×
2,425,833×
2,432,087×
2,370,632×
1,426,089×
984,333×
689,823×
713,162×
1,070,341×
1,050,499×
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×
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0×
1×
326,783×
2,266,924×
7,430,658×
14,713,694×
31,527,556×
53,698,524×
95,279,022×
156,647,872×
214,770,176×
288,525,898×
320,698,252×
382,536,978×
400,703,470×
423,974,672×
437,451,464×
403,504,736×
378,765,870×
375,127,424×
398,594,202×
423,815,482×
428,240,924×
476,122,918×
461,211,526×
461,394,586×
405,617,946×
358,910,346×
360,451,146×
393,732,482×
372,598,772×
387,341,510×
362,968,636×
277,658,342×
283,912,956×
240,070,068×
364,299,286×
385,921,012×
512,123,972×
538,652,446×
519,573,398×
479,467,326×
409,478,338×
390,249,094×
357,960,194×
277,832,458×
163,335,126×
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×