Base 30: 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
1.97 step
avg
6.17 step
avg
8.21 step
avg
6.82 step
avg
10.86 step
avg
56.75 step
avg
16.54 step
avg
56.36 step
avg
16.08 step
avg
112.11 step
avg
44.29 step
avg
97.87 step
avg
Step Frequency
Full Cycle
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29×
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29×



217×
210×
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269×
238×
474×
466×
454×
438×
418×
394×
366×
334×
298×
258×
214×
166×
114×
58×
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185×
674×
2,076×
5,736×
4,927×
17,056×
4,479×
3,891×
1,143×
752×
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1,239×
2,972×
3,610×
7,482×
14,552×
21,366×
22,268×
24,416×
23,914×
28,896×
34,308×
27,640×
22,334×
19,774×
15,156×
6,756×
1,572×
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269×



11,432×
29,976×
18,420×
9,266×
12,529×
13,145×
15,410×
13,918×
4,110×
9,051×
14,193×
24,985×
26,961×
14,973×
21,238×
28,091×
16,715×
17,102×
19,780×
27,565×
21,710×
15,243×
7,256×
2,616×


















16,169×
40,394×
36,807×
32,778×
37,898×
37,246×
42,690×
50,074×
54,208×
51,406×
38,276×
28,978×
29,907×
30,598×
22,193×
24,280×
19,045×
14,963×
15,722×
12,756×
21,093×
16,183×
18,973×
20,103×
30,363×
25,219×
28,433×
30,803×
22,851×
19,991×
15,512×
11,873×
11,167×
15,736×
14,698×
12,796×
10,774×
8,083×
10,549×
12,612×
17,124×
17,115×
22,340×
18,148×
10,974×
11,610×
13,790×
16,380×
8,992×
11,957×
11,663×
17,425×
21,070×
15,594×
7,052×
6,614×
3,802×
1,355×
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29×


17,480×
41,294×
72,922×
98,992×
173,234×
169,978×
269,264×
326,456×
459,164×
540,102×
597,250×
778,736×
973,644×
1,151,094×
985,404×
754,212×
540,198×
265,112×
93,918×
34,788×
4,408×
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2,229×
6,074×
5,376×
16,082×
11,711×
4,230×



31,056×
196,942×
267,272×
258,500×
388,704×
577,106×
695,929×
667,593×
580,714×
573,537×
794,608×
763,227×
787,497×
548,151×
565,247×
609,631×
683,382×
598,684×
511,431×
440,928×
559,879×
566,424×
518,567×
454,183×
552,448×
515,778×
487,568×
491,816×
552,902×
481,598×
523,624×
412,532×
429,378×
295,116×
355,952×
442,731×
324,557×
374,982×
500,228×
417,380×
417,372×
412,416×
344,889×
303,190×
385,922×
413,435×
429,356×
288,454×
303,231×
329,741×
357,801×
420,917×
407,047×
371,763×
350,275×
313,690×
297,445×
283,816×
291,011×
352,246×
374,059×
352,040×
312,361×
228,024×
187,878×
188,950×
173,092×
188,476×
225,942×
262,793×
195,335×
226,714×
209,887×
206,873×
213,944×
162,735×
167,296×
119,085×
132,624×
116,095×
120,318×
161,313×
226,985×
245,537×
302,614×
205,673×
164,041×
190,367×
182,208×
200,760×
242,184×
195,765×
153,790×
118,896×
163,557×
197,833×
210,777×
217,797×
191,610×
176,094×
229,386×
244,878×
240,959×
226,228×
160,951×
184,428×
258,118×
252,268×
209,142×
203,302×
152,705×
126,581×
119,853×
127,383×
103,747×
113,923×
131,971×
126,523×
76,064×
36,294×
25,473×
26,012×
33,078×
44,762×
45,016×
23,555×
16,620×
12,676×
9,591×
10,445×
2,586×
3,284×
394×
0s:
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14,675×
95,320×
412,088×
963,670×
2,785,816×
4,266,598×
4,999,442×
5,357,886×
5,289,816×
6,274,374×
10,057,570×
14,841,034×
17,937,410×
17,418,794×
15,584,216×
12,804,066×
7,471,408×
4,981,178×
3,504,832×
2,823,548×
2,266,618×
1,764,750×
1,340,368×
1,307,658×
2,258,458×
2,306,238×
3,093,286×
2,579,618×
1,861,014×
998,940×
753,472×
1,328,724×
1,102,288×
1,451,882×
608,766×
105,818×
0s:
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1,239×
2,200×
15,592×
148,744×
275,450×
152,278×
259,245×
349,715×
688,701×
282,592×
159,748×
180,011×
1,044,543×
1,905,881×
2,312,042×
2,350,048×
2,794,007×
3,801,474×
3,379,301×
3,466,639×
2,916,003×
2,560,036×
3,040,325×
3,330,718×
3,497,772×
3,944,075×
3,983,734×
2,891,328×
2,843,534×
2,864,538×
2,254,758×
2,426,466×
2,144,830×
1,937,445×
2,047,684×
2,085,900×
1,753,936×
1,504,765×
1,544,695×
1,698,909×
1,792,436×
1,699,430×
1,558,778×
873,881×
475,593×
458,244×
608,677×
704,966×
519,940×
234,201×
147,888×
101,368×
67,358×
88,994×
235,300×
757,234×
993,676×
572,625×
178,062×
101,814×
25,283×
21,523×
37,998×
46,847×
20,192×
3,936×
3,900×






















311,824×
3,644,056×
6,948,078×
6,889,823×
10,013,915×
13,625,958×
14,044,631×
13,974,280×
12,039,418×
10,576,705×
10,885,946×
11,267,776×
12,100,147×
12,719,916×
12,356,335×
9,998,785×
10,524,628×
11,110,162×
10,321,888×
8,322,485×
8,621,687×
8,862,917×
7,964,756×
8,329,046×
8,292,755×
7,224,620×
5,925,420×
5,314,344×
4,800,159×
4,495,191×
4,403,559×
4,114,145×
3,626,235×
3,046,108×
2,238,104×
2,287,724×
2,230,318×
2,977,029×
4,569,847×
5,672,295×
5,309,776×
5,458,505×
5,573,815×
6,954,750×
6,014,856×
8,060,097×
7,721,811×
7,631,123×
8,296,874×
7,479,096×
6,914,475×
7,623,512×
9,904,074×
12,718,658×
10,724,087×
9,167,444×
6,792,758×
7,663,266×
8,283,824×
7,149,230×
5,791,236×
5,617,016×
5,804,165×
4,661,985×
4,403,198×
4,335,059×
4,915,248×
6,032,507×
4,912,091×
4,203,563×
3,077,103×
3,267,850×
3,292,281×
2,905,004×
2,619,445×
2,133,396×
1,742,900×
1,388,684×
1,200,706×
1,908,738×
1,755,936×
2,135,128×
1,528,334×
1,372,847×
1,032,755×
847,526×
495,328×
504,935×
598,302×
408,708×
188,393×
114,999×
134,969×
188,747×
188,290×
133,250×
139,229×
115,861×
92,627×
75,032×
66,997×
33,844×
45,260×
13,520×
2,680×
19,232×
14,400×
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41,109×
424,332×
1,856,808×
4,618,384×
8,153,770×
10,779,312×
8,494,594×
4,310,174×
2,056,898×
1,685,648×
1,139,040×
299,264×
183,312×
45,036×










847,190×
6,054,766×
18,031,040×
30,979,716×
44,557,644×
65,247,044×
82,749,222×
105,995,434×
106,607,116×
97,392,032×
89,675,466×
89,543,944×
73,302,766×
62,946,968×
50,591,290×
51,540,652×
53,436,238×
58,292,788×
73,423,998×
81,942,920×
82,359,028×
71,482,110×
61,267,700×
55,012,412×
45,572,142×
41,392,952×
42,684,948×
49,514,850×
56,736,818×
55,324,752×
48,415,654×
42,536,006×
45,452,468×
61,675,946×
48,848,912×
33,956,568×
28,753,262×
28,649,526×
29,096,606×
33,845,156×
23,752,550×
15,939,172×
11,173,496×
5,939,034×
3,627,754×
1,388,516×
143,266×
13,920×
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269×




49,700×
638,356×
1,607,592×
1,201,638×
1,093,302×
1,342,634×
370,993×
355,165×
551,802×
394,198×
274,739×
179,755×
210,120×
161,750×
636,083×
7,173,714×
16,020,764×
16,787,836×
23,607,764×
32,251,521×
33,636,098×
38,536,388×
39,909,058×
43,995,022×
47,436,275×
40,018,881×
45,961,164×
44,236,712×
47,651,990×
46,337,034×
44,491,605×
40,455,090×
48,404,446×
46,826,243×
55,244,873×
49,338,030×
39,441,970×
37,021,102×
44,710,500×
46,951,748×
46,461,996×
51,186,688×
47,220,710×
50,977,235×
53,445,575×
54,632,833×
53,127,484×
53,877,480×
57,881,819×
51,035,133×
54,862,064×
45,937,610×
44,316,501×
36,291,614×
38,487,264×
33,215,663×
35,203,955×
35,504,531×
34,551,366×
27,691,846×
22,316,839×
22,724,031×
22,255,145×
22,286,006×
18,985,037×
29,338,020×
35,781,328×
39,140,750×
46,091,243×
55,566,922×
61,200,385×
58,984,775×
47,061,815×
47,223,038×
52,973,742×
56,065,165×
65,498,281×
60,512,717×
49,293,129×
45,140,385×
45,362,344×
45,993,134×
53,219,936×
54,093,228×
54,363,132×
51,409,501×
57,199,798×
64,467,698×
72,597,592×
97,600,956×
111,894,372×
104,213,235×
93,687,332×
86,969,815×
87,523,395×
85,807,232×
86,508,752×
76,160,645×
83,305,505×
96,393,853×
106,187,541×
91,541,850×
87,659,893×
85,336,581×
103,103,919×
104,876,359×
94,276,045×
83,009,493×
69,450,279×
64,421,141×
71,598,501×
74,837,512×
75,486,954×
77,410,437×
76,296,429×
71,676,268×
68,460,434×
75,942,315×
70,414,591×
68,965,176×
79,471,238×
89,324,754×
89,825,122×
94,373,050×
79,436,169×
74,328,404×
75,306,514×
79,914,554×
87,432,222×
96,991,689×
80,309,719×
72,049,747×
63,110,619×
53,310,486×
53,209,668×
54,433,122×
59,712,084×
57,602,638×
52,165,601×
46,952,539×
37,497,902×
47,342,701×
45,164,723×
36,781,221×
32,700,145×
31,905,888×
30,080,694×
30,749,572×
30,407,267×
25,042,656×
21,494,704×
22,599,890×
17,770,626×
15,582,904×
15,575,981×
14,201,224×
13,690,958×
15,736,103×
12,886,355×
7,793,895×
7,711,546×
9,754,333×
8,810,761×
7,176,019×
5,487,141×
5,053,025×
6,244,601×
7,469,317×
4,533,270×
2,032,686×
1,324,611×
1,622,150×
1,622,581×
1,270,806×
1,451,029×
651,118×
347,379×
168,524×
178,843×
81,540×
238,788×
441,744×
328,907×
154,880×
177,762×
94,362×
120,215×
211,470×
31,246×
13,700×