Base 22: 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 13 14 15
Average Steps
Full Cycle
1.95 step
avg
11.54 step
avg
6.67 step
avg
8.50 step
avg
9.13 step
avg
37.14 step
avg
14.79 step
avg
99.77 step
avg
32.15 step
avg
71.41 step
avg
18.95 step
avg
115.93 step
avg
53.12 step
avg
110.73 step
avg
34.33 step
avg
Step Frequency
Full Cycle
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21×
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21×









115×
110×
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153×
130×
258×
250×
238×
222×
202×
178×
150×
118×
82×
42×
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21×



640×
1,420×
5,720×
2,036×
1,751×
639×
422×
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21×
372×
1,578×
3,998×
4,130×
6,618×
8,836×
8,570×
10,798×
9,496×
6,756×
3,520×
1,086×
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153×










2,108×
4,548×
6,202×
2,711×
840×
44×
22×


3,770×
8,003×
7,718×
5,245×
4,053×
3,898×
4,860×
4,814×
4,920×
9,081×
7,330×
4,874×
8,704×
10,716×
9,682×
11,795×
14,141×
18,626×
19,669×
16,942×
15,297×
11,537×
9,998×
11,226×
13,138×
9,039×
5,869×
5,534×
5,728×
2,631×
3,534×
1,005×
972×
2,350×
1,428×
1,254×
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21×


5,514×
10,868×
19,802×
20,104×
37,796×
55,928×
65,012×
81,260×
94,008×
111,090×
126,556×
150,136×
132,868×
126,364×
69,870×
39,820×
18,170×
17,708×
902×
242×
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21×





3,558×
8,191×
4,110×
2,276×
2,248×
2,271×
344×





























































33,492×
140,698×
158,022×
168,215×
124,267×
152,942×
147,759×
149,098×
125,674×
111,818×
77,795×
65,951×
73,819×
59,091×
68,029×
75,309×
66,596×
73,049×
70,001×
78,042×
70,530×
77,425×
70,004×
78,022×
74,659×
72,394×
74,869×
92,288×
85,006×
97,732×
89,756×
90,158×
74,161×
80,808×
82,182×
81,435×
61,505×
46,436×
37,878×
19,924×
24,559×
20,388×
17,525×
19,991×
10,338×
9,408×
14,849×
12,721×
8,823×
17,665×
15,931×
19,612×
29,286×
39,815×
49,205×
62,101×
46,089×
35,211×
23,940×
19,582×
26,298×
19,613×
25,775×
19,155×
22,008×
15,007×
10,632×
19,708×
23,932×
34,139×
24,694×
14,902×
14,694×
11,947×
4,649×
4,892×
2,012×
1,190×
0s:
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3,653×
16,528×
55,678×
47,050×
92,732×
42,822×
34,848×
14,520×
9,724×
6,522×










68,434×
233,758×
413,042×
601,360×
700,328×
728,236×
711,558×
742,556×
733,122×
782,276×
905,202×
1,122,402×
1,348,544×
1,265,822×
813,790×
400,884×
249,540×
215,118×
331,842×
436,854×
371,762×
307,182×
227,768×
126,398×
81,776×
29,386×
26,054×
5,636×
2,442×
0s:
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21×












10,525×
50,470×
35,176×
26,691×
8,944×
14,218×
40,337×
156,419×
198,679×
156,449×
173,217×
133,789×
107,391×
157,863×
103,091×
106,533×
142,628×
247,969×
113,196×
70,276×
103,911×
172,944×
375,191×
485,264×
551,928×
504,545×
613,952×
772,504×
798,610×
788,641×
829,457×
876,859×
673,877×
618,780×
569,453×
638,117×
723,089×
791,776×
661,285×
488,824×
497,793×
720,285×
744,959×
660,208×
665,836×
526,206×
430,831×
476,891×
649,759×
570,818×
668,666×
704,180×
533,745×
390,118×
375,856×
553,262×
565,332×
595,059×
339,835×
343,696×
262,039×
278,874×
294,482×
268,606×
347,392×
361,580×
485,806×
498,381×
527,523×
526,771×
676,498×
751,443×
754,330×
889,564×
963,595×
665,423×
597,796×
493,514×
428,782×
368,246×
446,307×
340,971×
359,655×
454,073×
507,363×
445,036×
345,616×
349,630×
340,782×
262,049×
201,852×
155,720×
201,139×
203,167×
267,368×
288,638×
233,884×
182,908×
219,486×
233,023×
207,142×
243,531×
204,078×
188,802×
145,530×
135,028×
103,302×
97,367×
92,629×
164,840×
129,576×
102,157×
74,464×
72,213×
124,844×
122,682×
87,969×
46,351×
59,422×
68,263×
75,470×
25,438×
24,824×
19,224×
17,220×
43,028×
33,623×
12,458×
14,479×
16,698×
9,123×
3,641×
1,212×
0s:
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8,021×
42,908×
212,466×
418,396×
765,682×
1,500,922×
2,094,966×
2,611,708×
2,506,936×
3,883,148×
4,092,110×
5,065,936×
6,771,920×
8,780,790×
8,560,752×
8,587,940×
7,406,978×
8,750,340×
7,848,936×
7,576,428×
6,450,172×
5,605,054×
4,446,314×
4,726,642×
3,972,838×
3,479,580×
3,221,616×
2,781,876×
2,198,074×
1,732,146×
1,455,768×
845,314×
460,206×
128,066×
30,728×
2,802×
0s:
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153×





































35,515×
560,260×
1,115,666×
1,536,291×
1,420,486×
1,556,451×
1,464,911×
1,001,549×
826,053×
698,117×
458,926×
568,084×
353,289×
252,290×
253,363×
427,061×
699,505×
680,267×
706,468×
614,206×
542,762×
516,332×
583,286×
635,518×
666,302×
851,095×
596,838×
522,605×
670,855×
772,257×
1,282,383×
868,227×
2,184,081×
2,555,275×
4,289,512×
5,286,239×
5,770,651×
7,889,541×
7,538,033×
5,961,462×
4,710,054×
4,399,970×
4,794,191×
4,907,066×
5,947,908×
6,188,297×
5,093,725×
4,914,594×
5,772,592×
5,530,187×
6,226,427×
6,778,428×
6,496,529×
5,845,536×
5,070,159×
4,779,639×
4,771,340×
3,838,644×
3,781,497×
3,258,091×
3,265,814×
3,674,417×
4,238,813×
3,578,762×
2,949,317×
2,307,937×
2,707,432×
3,221,352×
3,706,801×
3,277,689×
2,872,382×
2,328,109×
1,914,883×
1,945,526×
2,368,953×
2,119,084×
1,852,571×
1,789,726×
1,829,959×
2,371,140×
2,667,147×
2,419,323×
2,229,391×
1,592,057×
991,921×
1,019,943×
882,828×
577,197×
521,853×
599,407×
579,330×
570,492×
528,433×
507,238×
450,393×
665,755×
770,891×
1,055,544×
1,300,371×
1,348,642×
1,298,742×
1,810,471×
1,644,470×
2,208,034×
2,103,255×
2,137,612×
2,474,815×
1,939,599×
1,993,489×
3,134,228×
4,789,245×
4,701,382×
3,764,259×
2,685,696×
1,868,478×
2,322,879×
2,910,798×
2,195,872×
2,030,908×
1,293,311×
1,176,777×
1,180,593×
1,139,881×
1,434,097×
1,794,912×
1,531,263×
974,847×
653,261×
893,467×
916,927×
708,479×
528,838×
508,638×
469,529×
622,990×
667,622×
725,002×
795,754×
882,952×
936,609×
1,040,581×
967,342×
1,685,149×
2,301,954×
2,452,829×
2,139,050×
1,715,478×
1,650,779×
1,694,104×
1,640,491×
2,295,408×
2,310,278×
2,022,773×
1,294,846×
992,578×
1,106,900×
1,011,888×
888,132×
872,324×
577,686×
382,341×
456,630×
803,867×
755,725×
540,252×
837,611×
702,664×
544,450×
441,100×
709,533×
888,801×
1,491,294×
777,792×
736,388×
509,502×
216,025×
305,243×
289,164×
285,430×
159,141×
120,832×
91,080×
159,737×
71,688×
24,161×
18,814×
39,010×
17,792×
1,515×
3,901×
8,433×
990×
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8,021×
84,540×
333,460×
375,964×
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3,383,176×
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1,977,114×
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910,388×
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342,938×
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613,950×
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3,420,870×
3,127,396×
1,364,376×
818,942×
301,284×
145,588×
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32,544×
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15,546×
207,168×
720,706×
94,258×
99,231×
67,301×
32,461×
130,768×
129,551×
78,463×
240,001×
460,242×
311,826×
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533,430×
802,755×
1,011,001×
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1,209,053×
1,616,523×
1,261,215×
772,369×
690,637×
581,268×
628,135×
650,800×
2,284,364×
3,040,181×
4,172,563×
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5,566,228×
7,938,800×
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9,677,861×
9,476,188×
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7,854,101×
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4,536,758×
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5,738,112×
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9,566,521×
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669,268×
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544,248×
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1,144×
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35,801×
440,536×
1,588,560×
2,763,400×
4,107,838×
8,693,260×
20,717,856×
22,277,882×
24,023,494×
30,069,466×
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181,888,306×
201,402,042×
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229,762,514×
208,978,964×
210,873,924×
159,729,450×
128,451,880×
125,023,822×
117,744,402×
118,422,130×
118,564,548×
137,648,472×
126,958,640×
124,564,700×
106,386,296×
82,492,312×
84,605,242×
79,814,462×
78,115,006×
84,818,240×
89,168,710×
79,803,258×
65,310,774×
51,410,040×
41,754,640×
34,182,986×
20,735,500×
12,925,996×
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11,162,908×
10,326,184×
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14,070,596×
12,485,712×
13,288,402×
13,850,614×
19,229,938×
24,040,148×
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25,027,148×
31,290,422×
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18,091,472×
15,504,158×
10,645,314×
6,478,098×
4,132,072×
2,236,172×
2,089,360×
1,388,270×
908,568×
2,139,096×
6,826,174×
5,941,418×
4,766,758×
2,586,764×
933,024×
170,962×