Base 54: 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		1.46 step
avg		11.75 step
avg		3.00 step
avg		13.94 step
avg		43.89 step
avg		16.22 step
avg		100.96 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
53×
0s:
1s:
2s:
15×
768×
702×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
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17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
1×
809×
754×
1,506×
1,498×
1,486×
1,470×
1,450×
1,426×
1,398×
1,366×
1,330×
1,290×
1,246×
1,198×
1,146×
1,090×
1,030×
966×
898×
826×
750×
670×
586×
498×
406×
310×
210×
106×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
1×
23,349×
60,996×
244,296×
32,348×
28,195×
3,519×
2,306×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
1×
8,763×
10,912×
16,442×
36,442×
59,418×
104,596×
129,550×
192,906×
206,044×
323,688×
330,588×
384,084×
321,272×
391,434×
357,328×
345,124×
297,772×
288,800×
215,898×
183,662×
141,254×
111,788×
77,018×
35,696×
10,526×
1,110×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
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17s:
18s:
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51s:
52s:
53s:
54s:
55s:
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57s:
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59s:
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68s:
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71s:
72s:
73s:
74s:
75s:
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77s:
78s:
79s:
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81s:
82s:
83s:
84s:
85s:
86s:
87s:
88s:
89s:
90s:
91s:
92s:
93s:
94s:
95s:
96s:
97s:
98s:
99s:
100s:
101s:
102s:
103s:
104s:
105s:
106s:
107s:
108s:
109s:
110s:
111s:
112s:
113s:
114s:
115s:
116s:
117s:
118s:
119s:
120s:
121s:
122s:
123s:
124s:
125s:
126s:
127s:
128s:
129s:
130s:
131s:
132s:
133s:
134s:
135s:
136s:
137s:
138s:
139s:
140s:
141s:
142s:
143s:
144s:
145s:
146s:
147s:
148s:
149s:
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151s:
152s:
153s:
154s:
155s:
156s:
157s:
158s:
159s:
160s:
161s:
162s:
163s:
164s:
165s:
166s:
167s:
168s:
169s:
170s:
1×
297,192×
734,295×
687,963×
727,354×
936,331×
960,734×
1,022,888×
1,012,886×
928,742×
835,361×
710,580×
780,317×
777,289×
845,639×
745,140×
742,567×
765,191×
809,310×
758,009×
669,552×
713,870×
631,582×
772,025×
964,923×
852,211×
634,008×
554,518×
376,526×
404,764×
412,207×
527,223×
444,580×
378,944×
345,502×
389,473×
419,130×
412,590×
384,803×
392,686×
424,111×
461,296×
594,675×
559,080×
553,344×
579,862×
396,627×
400,614×
426,280×
371,639×
327,858×
439,099×
353,625×
381,135×
405,245×
448,580×
317,102×
288,266×
286,116×
289,387×
325,716×
364,188×
399,929×
274,625×
193,049×
249,516×
220,076×
177,314×
158,711×
166,395×
155,694×
94,025×
131,299×
138,292×
80,640×
103,393×
90,242×
73,780×
97,132×
64,282×
55,310×
49,416×
59,793×
41,527×
24,934×
61,717×
74,032×
75,956×
82,612×
97,113×
104,786×
131,196×
120,642×
153,243×
154,063×
110,476×
161,610×
209,177×
175,807×
218,767×
204,077×
131,476×
121,172×
96,860×
130,864×
130,272×
96,322×
76,320×
76,062×
59,716×
51,858×
49,482×
67,629×
82,332×
51,269×
78,276×
38,752×
38,228×
42,266×
46,810×
26,807×
34,070×
29,094×
59,880×
55,704×
73,611×
87,435×
125,366×
62,015×
59,613×
101,203×
107,391×
118,447×
141,096×
105,607×
133,088×
135,572×
105,679×
78,064×
74,383×
71,619×
89,383×
123,438×
114,425×
123,816×
110,724×
133,392×
152,918×
200,488×
115,622×
158,054×
98,751×
62,414×
21,602×
25,876×
21,210×
11,970×
15,318×
9,144×
6,606×
6,672×
9,100×
9,272×
18,030×
24,388×
10,432×
14,184×
22,876×
39,802×
37,986×
30,472×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
1×
161,767×
431,264×
966,226×
1,302,768×
1,926,766×
3,034,220×
4,434,504×
6,288,130×
8,824,000×
11,197,750×
15,090,468×
18,249,336×
23,698,022×
29,188,366×
31,721,692×
34,494,258×
37,900,704×
34,360,866×
32,320,356×
30,805,334×
23,237,176×
15,018,054×
10,749,266×
6,264,774×
2,917,796×
1,007,528×
355,214×
230,482×
28,376×
1,456×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
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86s:
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91s:
92s:
93s:
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96s:
97s:
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102s:
103s:
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106s:
107s:
108s:
109s:
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111s:
112s:
113s:
114s:
115s:
116s:
117s:
118s:
119s:
120s:
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133s:
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135s:
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137s:
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143s:
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171s:
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174s:
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235s:
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244s:
245s:
246s:
247s:
248s:
249s:
250s:
251s:
252s:
253s:
254s:
255s:
256s:
257s:
258s:
259s:
260s:
261s:
262s:
263s:
264s:
265s:
266s:
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290s:
291s:
292s:
293s:
294s:
295s:
296s:
297s:
298s:
299s:
300s:
301s:
1×
2,636,791×
12,233,431×
11,884,013×
18,434,376×
20,350,310×
19,980,317×
20,906,075×
21,120,842×
21,393,270×
22,021,931×
21,769,450×
21,341,525×
20,886,313×
19,164,094×
19,661,253×
17,562,770×
15,721,532×
14,238,613×
13,650,612×
15,505,580×
15,030,963×
13,290,645×
12,958,976×
12,084,881×
12,353,438×
12,209,121×
12,784,931×
13,252,571×
13,062,567×
12,813,845×
11,964,701×
10,908,025×
10,758,584×
10,822,375×
10,023,443×
10,149,778×
10,601,546×
11,282,781×
10,644,383×
9,985,768×
11,478,636×
14,232,216×
14,320,295×
14,398,472×
12,830,563×
12,677,990×
11,426,294×
11,404,820×
11,027,340×
9,322,553×
10,927,786×
12,022,000×
11,719,507×
10,272,426×
9,117,840×
10,472,121×
11,405,910×
11,858,417×
14,050,166×
13,716,493×
14,538,259×
13,909,581×
14,233,432×
12,784,151×
11,911,219×
10,972,706×
11,913,407×
11,748,703×
15,761,526×
15,180,496×
14,869,562×
14,322,526×
14,546,276×
16,248,959×
17,820,114×
18,452,137×
19,132,063×
20,538,525×
21,124,621×
20,465,818×
20,755,097×
22,190,199×
22,303,217×
22,660,265×
22,576,186×
21,702,438×
21,467,736×
20,405,306×
20,125,424×
18,895,426×
19,307,125×
18,679,980×
18,534,063×
19,639,452×
19,048,610×
19,066,393×
19,589,615×
21,113,025×
22,698,679×
22,295,378×
23,200,970×
20,800,145×
19,376,062×
18,230,081×
18,348,789×
18,794,931×
19,391,018×
17,663,524×
16,801,228×
14,833,413×
14,927,151×
16,262,530×
18,019,792×
18,278,498×
16,525,878×
16,904,992×
16,981,789×
16,518,544×
14,731,098×
15,324,379×
14,927,872×
13,163,381×
13,978,732×
15,407,096×
15,013,782×
14,525,842×
13,942,474×
15,026,304×
14,272,791×
11,954,651×
13,911,387×
13,889,916×
14,902,320×
13,312,749×
12,377,241×
12,776,355×
13,706,548×
12,450,404×
12,155,612×
11,432,303×
12,384,834×
11,738,646×
9,628,158×
9,570,053×
8,857,725×
9,523,969×
10,042,773×
10,609,261×
11,140,562×
11,323,227×
11,610,388×
12,077,721×
11,173,774×
11,049,108×
11,763,361×
13,311,162×
12,439,767×
12,418,116×
12,823,518×
14,036,133×
14,360,125×
13,615,393×
13,275,857×
13,430,187×
12,656,846×
12,020,323×
13,978,686×
14,466,229×
15,355,111×
14,080,369×
11,449,605×
10,075,056×
9,810,882×
11,212,997×
13,120,501×
10,986,709×
9,694,902×
8,640,664×
9,256,336×
8,609,241×
6,290,634×
6,588,636×
6,877,070×
6,877,917×
5,171,019×
5,899,056×
6,017,883×
5,379,268×
4,846,830×
5,952,643×
5,879,531×
6,658,948×
6,490,160×
6,047,634×
5,252,192×
5,273,257×
4,329,624×
4,807,629×
4,049,034×
3,982,795×
3,412,644×
3,978,434×
3,525,985×
3,212,997×
3,777,439×
4,368,978×
5,255,326×
4,692,607×
5,189,432×
4,384,833×
4,121,487×
3,654,259×
3,020,018×
4,053,058×
3,808,002×
4,037,631×
3,262,741×
3,030,168×
2,593,717×
2,921,971×
2,307,116×
2,101,787×
2,098,545×
2,372,735×
2,832,572×
2,588,638×
2,074,764×
2,105,735×
2,426,475×
3,190,928×
3,803,579×
4,260,224×
3,612,736×
2,722,910×
2,574,688×
3,715,235×
3,463,598×
2,878,794×
2,114,958×
1,934,248×
2,181,179×
1,076,763×
1,281,408×
1,666,036×
1,867,174×
1,914,707×
1,855,269×
1,737,860×
1,107,006×
1,444,251×
1,217,750×
995,080×
1,089,338×
1,183,539×
945,071×
1,162,664×
806,318×
916,165×
744,742×
1,229,939×
1,269,350×
879,051×
942,106×
1,253,754×
1,753,188×
1,673,574×
780,499×
1,206,526×
1,429,609×
1,728,171×
1,173,199×
927,463×
967,873×
886,237×
533,218×
590,037×
1,045,971×
1,108,821×
1,319,171×
771,386×
638,214×
1,005,725×
940,930×
865,999×
884,703×
860,780×
409,751×
462,583×
573,227×
433,994×
365,080×
394,037×
272,922×
506,017×
372,792×
238,301×
210,142×
154,755×
43,246×
21,008×
41,536×