Base 59: 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
Average Steps
Full Cycle		1.98 step
avg		5.86 step
avg		14.19 step
avg		30.81 step
avg		16.55 step
avg		114.79 step
avg		24.74 step
avg		230.80 step
avg
Step Frequency
Full Cycle
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0×
1×
58×
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0×
2×
97×
117×
164×
338×
356×
232×
464×
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0×
1×
58×
1,799×
896×
1,790×
1,780×
1,766×
1,748×
1,726×
1,700×
1,670×
1,636×
1,598×
1,556×
1,510×
1,460×
1,406×
1,348×
1,286×
1,220×
1,150×
1,076×
998×
916×
830×
740×
646×
548×
446×
340×
230×
116×
0s:
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0×
1×
58×
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0×
0×
0×
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0×
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0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
133,980×
394,226×
28,681×
899×
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0×
1×
58×
0×
0×
33,520×
43,098×
53,060×
120,844×
165,236×
262,822×
281,797×
427,760×
437,650×
613,591×
565,012×
640,670×
498,695×
558,638×
466,573×
406,674×
373,395×
303,301×
255,504×
175,126×
121,613×
82,758×
74,347×
49,742×
17,362×
0s:
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0×
1×
58×
20,468×
62,220×
191,998×
777,081×
250,943×
137,905×
109,136×
117,381×
191,017×
365,709×
291,675×
216,838×
195,386×
176,055×
223,267×
208,158×
206,340×
205,899×
62,759×
154,658×
101,540×
75,336×
148,641×
125,990×
195,298×
124,574×
235,055×
442,013×
1,060,565×
574,220×
453,919×
476,284×
375,454×
312,615×
479,329×
591,570×
471,401×
644,227×
478,482×
340,967×
366,423×
464,432×
400,132×
279,223×
214,283×
271,715×
362,707×
406,757×
378,932×
365,920×
328,036×
442,037×
382,742×
486,968×
394,514×
289,493×
237,428×
236,923×
188,414×
104,140×
182,651×
225,587×
296,975×
176,370×
207,708×
153,592×
55,876×
58,805×
89,917×
113,279×
105,572×
99,357×
190,314×
189,443×
119,668×
131,747×
94,248×
229,863×
449,284×
335,569×
208,861×
162,549×
159,668×
154,317×
240,427×
175,045×
140,367×
151,796×
71,296×
44,336×
114,355×
48,955×
45,587×
26,152×
12,322×
34,078×
98,778×
67,016×
65,144×
135,354×
233,797×
223,092×
165,264×
148,563×
79,457×
24,272×
31,417×
43,844×
86,620×
43,814×
28,675×
39,143×
35,411×
31,773×
20,685×
740×
0×
301,525×
788,915×
1,699,031×
4,729,125×
1,968,362×
1,708,117×
1,516,585×
1,443,781×
1,017,316×
823,038×
754,715×
903,088×
798,946×
538,879×
505,247×
713,367×
689,522×
776,470×
833,751×
781,187×
780,270×
629,765×
654,887×
772,260×
865,243×
501,013×
548,051×
655,335×
578,487×
654,351×
723,991×
528,348×
389,232×
553,129×
781,110×
715,182×
850,260×
707,573×
690,448×
456,044×
381,272×
354,428×
525,805×
517,600×
875,103×
804,702×
584,105×
345,832×
269,075×
339,009×
291,439×
247,593×
405,415×
488,122×
283,340×
145,738×
76,185×
256,808×
205,442×
148,755×
155,388×
117,726×
112,100×
147,503×
102,093×
80,252×
68,993×
97,808×
57,968×
59,754×
50,464×
79,090×
93,345×
64,813×
55,208×
92,088×
163,289×
132,340×
182,134×
128,587×
80,841×
170,738×
229,019×
124,430×
203,812×
95,021×
49,743×
38,236×
37,467×
45,312×
100,819×
96,212×
76,551×
81,971×
90,902×
136,422×
137,009×
186,591×
213,654×
150,830×
203,396×
124,778×
86,168×
102,367×
83,620×
54,330×
100,039×
77,077×
8,094×
17,803×
16,077×
25,754×
147,103×
101,793×
38,581×
18,347×
23,245×
17,736×
18,536×
26,124×
29,703×
11,923×
2,322×
8,349×
420×
0s:
1s:
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44s:
45s:
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47s:
48s:
0×
1×
58×
0×
0×
0×
0×
0×
0×
451,152×
1,150,620×
2,544,449×
4,389,991×
7,037,523×
10,108,229×
13,492,529×
18,226,271×
25,308,200×
31,458,636×
36,348,811×
44,139,218×
45,895,862×
49,600,167×
48,715,689×
53,595,700×
45,759,498×
41,171,427×
32,317,880×
24,172,008×
18,768,044×
14,153,714×
13,590,725×
11,250,117×
11,983,718×
9,861,621×
9,936,422×
10,588,178×
11,302,549×
10,300,973×
9,242,824×
7,698,373×
7,516,539×
5,699,216×
4,139,422×
1,937,701×
1,598,393×
595,422×
128,890×
13,800×
0s:
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0×
1×
58×
0×
0×
55,096×
153,494×
841,078×
1,512,032×
3,304,524×
1,678,122×
1,873,404×
970,746×
560,050×
1,058,181×
1,882,162×
846,542×
1,065,980×
1,007,153×
616,166×
6,193×
3,546×
9,169×
12,011×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
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2,212,695×
10,088,834×
49,015,223×
64,474,055×
68,267,112×
71,788,320×
69,261,182×
64,489,511×
66,752,764×
66,997,095×
67,672,134×
62,968,800×
56,908,539×
58,405,037×
60,854,667×
56,452,136×
60,674,417×
67,472,696×
69,114,734×
68,585,043×
53,683,484×
47,972,993×
49,336,609×
56,373,803×
57,603,962×
71,596,876×
74,944,928×
63,865,364×
70,191,579×
71,836,691×
79,288,393×
71,545,578×
69,523,683×
60,691,235×
67,824,403×
70,296,713×
66,817,677×
55,682,159×
54,403,101×
66,523,223×
59,157,726×
59,957,934×
55,765,387×
58,203,767×
55,861,596×
50,985,272×
57,197,742×
62,795,160×
65,825,871×
75,487,866×
68,929,879×
67,424,039×
61,538,761×
61,548,081×
58,246,437×
52,934,903×
56,307,503×
46,100,770×
42,305,066×
42,536,884×
53,857,548×
49,531,133×
56,098,972×
47,951,922×
51,920,404×
46,201,220×
44,788,509×
43,567,682×
51,319,005×
46,707,382×
45,119,379×
46,143,178×
45,345,643×
44,373,911×
45,500,595×
44,900,819×
48,329,628×
50,243,470×
49,765,731×
43,759,341×
41,517,127×
38,048,040×
32,471,520×
33,163,323×
23,185,310×
22,766,375×
20,169,307×
20,225,553×
17,626,005×
25,800,680×
20,925,509×
22,203,292×
20,703,609×
20,903,443×
22,999,912×
21,547,924×
19,258,575×
16,203,144×
20,667,334×
21,571,803×
22,214,962×
22,691,401×
16,307,738×
18,530,490×
20,564,906×
19,461,579×
22,664,599×
16,374,199×
12,565,246×
15,643,182×
12,910,659×
11,574,173×
11,383,721×
10,587,344×
7,478,737×
5,977,807×
4,506,845×
5,395,822×
4,652,781×
3,977,849×
6,123,531×
6,563,322×
9,681,682×
8,108,569×
9,377,195×
7,311,299×
8,147,724×
10,039,516×
9,344,135×
16,431,055×
14,336,651×
9,719,473×
10,398,470×
7,604,658×
4,298,776×
5,774,938×
7,427,679×
7,335,473×
7,110,328×
5,716,715×
11,039,313×
12,096,450×
8,608,914×
11,707,355×
13,336,315×
11,191,709×
8,493,943×
11,518,461×
13,343,076×
11,402,311×
11,412,960×
9,460,289×
7,294,771×
5,832,017×
3,183,296×
3,296,872×
3,094,593×
2,811,636×
1,532,505×
1,241,064×
1,414,542×
1,187,911×
803,968×
1,304,293×
1,367,486×
1,913,781×
1,893,040×
3,037,505×
2,986,670×
2,546,936×
2,227,215×
3,379,763×
4,714,914×
2,057,726×
1,276,785×
862,211×
1,530,493×
2,683,867×
2,704,778×
2,297,517×
856,579×
1,564,533×
3,923,688×
2,982,561×
5,132,815×
5,991,488×
5,105,156×
4,420,907×
3,901,792×
2,911,719×
1,620,681×
1,223,036×
803,751×
1,984,219×
955,235×
980,580×
663,316×
649,747×
397,324×
359,094×
189,380×
81,478×
34,149×
27,355×