Base 60: 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
Average Steps
Cycle Start		0.98 step
avg		1.47 step
avg		12.89 step
avg		4.52 step
avg		14.96 step
avg		42.18 step
avg		11.91 step
avg		135.02 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
59×
0s:
1s:
2s:
16×
944×
870×
0s:
1s:
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31s:
1×
989×
928×
1,854×
1,846×
1,834×
1,818×
1,798×
1,774×
1,746×
1,714×
1,678×
1,638×
1,594×
1,546×
1,494×
1,438×
1,378×
1,314×
1,246×
1,174×
1,098×
1,018×
934×
846×
754×
658×
558×
454×
346×
234×
118×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
1×
8,571×
20,076×
80,640×
322,560×
39,368×
35,335×
65,448×
6,128×
2,456×
4,588×
1,648×
3,202×
5,644×
0s:
1s:
2s:
3s:
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21s:
22s:
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26s:
27s:
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29s:
1×
11,607×
14,294×
21,950×
48,482×
79,380×
139,350×
173,532×
257,888×
249,910×
434,280×
494,610×
579,884×
491,728×
635,960×
508,176×
580,436×
509,082×
516,970×
411,658×
393,194×
302,308×
252,210×
194,968×
150,380×
104,454×
50,426×
15,262×
2,014×
118×
0s:
1s:
2s:
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102s:
103s:
104s:
105s:
106s:
107s:
108s:
109s:
110s:
111s:
112s:
1×
371,372×
900,164×
821,267×
889,715×
1,025,156×
1,242,512×
1,165,609×
1,198,978×
1,257,195×
1,203,589×
1,124,334×
893,015×
829,084×
826,861×
945,673×
859,160×
920,386×
867,622×
834,345×
972,640×
1,115,248×
1,059,479×
1,100,184×
1,178,566×
1,317,817×
1,190,822×
1,086,295×
1,196,606×
1,295,861×
1,103,243×
1,069,934×
887,491×
886,862×
951,146×
999,879×
997,349×
990,517×
1,044,078×
1,139,598×
1,146,082×
1,185,015×
1,256,916×
1,129,309×
1,305,147×
1,273,997×
1,231,200×
1,036,099×
1,292,094×
1,184,590×
1,196,040×
1,280,042×
1,222,129×
1,107,562×
941,973×
1,057,644×
1,105,308×
1,181,376×
1,094,416×
1,032,377×
935,118×
960,420×
911,277×
977,730×
847,933×
734,825×
669,847×
491,348×
553,930×
532,593×
521,324×
495,665×
435,519×
362,513×
398,014×
401,615×
410,757×
333,526×
356,635×
259,917×
331,067×
304,787×
323,290×
392,476×
379,571×
349,598×
444,109×
357,244×
318,744×
276,625×
277,392×
292,958×
224,017×
201,124×
232,057×
132,553×
110,800×
159,402×
155,394×
203,202×
256,159×
274,999×
302,326×
298,911×
292,562×
340,287×
256,487×
212,158×
102,542×
54,808×
49,972×
39,022×
42,762×
0s:
1s:
2s:
3s:
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5s:
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16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
1×
1,210,979×
3,193,092×
7,153,930×
11,188,652×
17,966,302×
24,537,592×
32,077,946×
45,194,078×
57,692,072×
70,428,060×
75,678,048×
85,827,530×
75,913,734×
70,430,786×
64,753,714×
52,131,370×
37,512,088×
20,350,238×
11,607,856×
7,123,928×
4,109,944×
1,619,400×
1,046,204×
33,440×
8,456×
0s:
1s:
2s:
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381s:
382s:
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384s:
385s:
1×
946,614×
4,916,589×
4,566,945×
5,306,802×
5,870,970×
5,734,125×
5,361,359×
4,909,631×
4,854,113×
5,194,619×
6,831,070×
7,587,548×
9,191,835×
8,160,118×
8,343,035×
9,228,344×
11,482,204×
11,829,770×
12,761,148×
13,849,988×
16,985,923×
17,711,826×
14,604,019×
12,657,622×
12,355,972×
13,378,987×
16,807,202×
15,729,565×
17,039,119×
18,023,354×
19,033,638×
18,077,601×
17,800,873×
19,748,984×
21,682,645×
20,609,013×
22,008,929×
24,641,656×
27,015,926×
26,053,751×
27,865,223×
26,686,260×
27,453,863×
30,781,551×
34,925,662×
34,403,842×
33,460,121×
29,991,040×
29,437,249×
26,502,968×
27,401,615×
29,336,236×
30,110,393×
29,067,512×
25,111,371×
25,856,214×
24,939,913×
25,512,483×
27,178,549×
28,598,585×
29,072,148×
31,298,514×
30,668,025×
30,001,572×
31,091,537×
29,480,171×
33,841,331×
33,768,376×
36,586,182×
38,445,980×
38,909,735×
36,222,336×
33,372,458×
31,123,081×
30,555,612×
30,399,431×
32,114,724×
34,995,189×
39,311,613×
42,021,826×
41,345,489×
41,653,251×
42,760,297×
38,402,188×
43,951,362×
41,994,444×
38,571,666×
39,092,225×
38,572,735×
38,677,559×
35,452,755×
33,358,944×
30,908,160×
30,342,847×
30,350,589×
31,101,883×
32,846,283×
32,221,111×
31,273,051×
31,830,856×
32,647,730×
30,679,260×
28,311,232×
30,396,786×
32,337,046×
29,521,432×
28,308,419×
27,005,634×
28,178,957×
30,363,340×
30,710,827×
32,679,665×
37,526,629×
35,716,723×
35,072,047×
35,098,818×
36,429,609×
34,954,738×
33,783,746×
33,984,836×
33,186,999×
30,486,165×
30,346,467×
31,918,491×
34,455,861×
34,890,239×
34,713,646×
33,001,471×
36,223,696×
33,268,510×
32,700,704×
32,964,284×
32,133,958×
31,584,406×
33,532,826×
32,834,323×
29,646,213×
28,397,882×
27,159,036×
27,720,110×
28,039,542×
31,789,778×
38,049,820×
37,339,891×
35,699,055×
31,805,037×
31,322,676×
27,818,047×
24,682,300×
21,196,780×
21,795,589×
24,016,129×
22,527,838×
23,920,486×
26,176,899×
26,309,905×
22,725,493×
21,100,919×
21,967,419×
21,403,025×
23,048,917×
22,702,211×
23,976,938×
22,571,863×
19,434,035×
17,688,638×
17,651,884×
16,916,772×
20,167,961×
21,036,142×
20,213,021×
19,183,182×
19,480,589×
20,899,604×
21,638,181×
24,327,614×
20,956,848×
23,776,350×
21,283,350×
20,690,640×
18,794,077×
20,727,291×
21,770,522×
21,740,958×
19,647,201×
17,045,787×
16,396,220×
17,388,871×
18,452,041×
20,268,341×
17,899,596×
17,711,371×
17,729,243×
15,970,016×
17,597,244×
19,120,129×
18,083,539×
16,327,457×
15,418,582×
15,456,768×
13,964,173×
14,484,535×
14,996,280×
16,356,622×
17,109,928×
19,671,047×
21,674,237×
21,838,251×
20,075,513×
20,332,570×
20,622,836×
23,097,256×
25,671,779×
23,464,650×
21,763,748×
23,465,257×
23,630,080×
25,428,584×
25,356,638×
23,973,263×
24,792,710×
24,851,101×
22,262,902×
20,480,404×
20,218,380×
22,541,460×
24,180,515×
23,572,730×
21,885,158×
23,422,217×
22,565,047×
21,761,028×
19,950,410×
15,477,617×
14,132,749×
13,128,234×
12,655,977×
12,886,093×
12,848,354×
12,947,598×
13,414,270×
13,938,388×
11,267,807×
11,396,098×
12,128,794×
13,929,019×
13,722,424×
11,612,411×
10,669,787×
11,485,622×
10,394,247×
9,432,535×
9,568,006×
11,137,989×
10,380,204×
9,686,550×
9,781,844×
11,437,663×
12,241,188×
12,540,162×
12,154,427×
9,581,567×
8,479,658×
7,089,608×
7,878,199×
8,577,345×
8,034,715×
6,754,918×
6,207,657×
6,836,739×
6,824,003×
7,456,118×
5,631,440×
6,415,700×
5,843,004×
7,568,141×
6,817,113×
7,246,501×
6,608,673×
7,887,493×
7,720,407×
9,009,015×
9,996,190×
11,027,361×
8,728,241×
8,386,634×
9,158,225×
8,965,542×
7,755,720×
7,177,259×
6,716,533×
7,359,725×
5,583,425×
4,170,810×
4,250,035×
4,269,624×
3,490,577×
2,769,926×
3,765,795×
3,981,462×
2,665,776×
2,258,115×
2,427,772×
2,249,045×
1,562,931×
1,638,562×
2,397,364×
1,558,451×
1,413,426×
965,874×
573,304×
646,379×
431,971×
560,382×
892,008×
1,477,155×
2,057,673×
2,463,158×
1,790,900×
1,143,432×
1,338,868×
1,238,350×
1,381,955×
1,494,211×
1,501,453×
2,135,078×
2,074,510×
1,855,451×
2,267,858×
1,925,804×
1,699,191×
942,546×
921,659×
1,463,146×
2,215,765×
1,937,495×
2,393,155×
2,367,466×
1,531,796×
1,235,114×
2,186,860×
1,766,362×
2,238,923×
1,481,868×
1,865,211×
1,288,121×
1,037,950×
1,219,700×
1,130,663×
1,961,410×
2,170,792×
2,221,532×
1,331,758×
1,329,164×
1,367,678×
1,470,563×
1,501,645×
1,852,913×
1,700,308×
1,932,581×
1,437,418×
1,296,735×
826,565×
1,104,264×
835,016×
543,888×
447,682×
448,097×
158,379×
23,126×
108,990×
227,094×
93,904×
92,662×
36,808×
205,428×
237,342×
77,962×
151,057×
185,099×
247,033×
159,398×
129,748×
4,632×
3,216×