Base 34: Iteration Frequencies: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl

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
Average Steps
Full Cycle		1.97 step
avg		10.21 step
avg		8.97 step
avg		6.92 step
avg		11.30 step
avg		66.48 step
avg		16.89 step
avg		48.10 step
avg		32.25 step
avg		64.30 step
avg		66.00 step
avg
Step Frequency
Full Cycle
0s:
1s:
2s:
0×
1×
33×
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0×
1×
34×
41×
81×
42×
0×
0×
0×
0×
0×
0×
6×
186×
204×
0s:
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0×
1×
339×
304×
606×
598×
586×
570×
550×
526×
498×
466×
430×
390×
346×
298×
246×
190×
130×
66×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
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9s:
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11s:
0×
1×
33×
480×
1,336×
8,384×
8,801×
32,204×
6,782×
5,475×
1,449×
1,100×
0s:
1s:
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0×
1×
33×
882×
5,352×
14,058×
13,782×
17,318×
34,186×
47,484×
63,224×
60,892×
66,856×
52,074×
52,710×
34,546×
22,116×
12,332×
4,096×
0s:
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108s:
109s:
110s:
0×
1×
1,439×
1,850×
2,748×
6,032×
16,516×
19,046×
26,440×
27,720×
24,310×
36,915×
22,481×
25,945×
18,686×
11,513×
8,737×
10,176×
16,615×
14,314×
12,450×
16,284×
7,795×
9,523×
12,018×
10,360×
6,268×
7,182×
5,636×
12,286×
10,329×
16,400×
10,350×
6,602×
10,960×
10,170×
13,594×
8,939×
12,336×
16,696×
15,618×
25,342×
16,819×
12,254×
7,554×
0×
0×
28,597×
70,671×
73,503×
40,237×
39,790×
55,047×
46,330×
30,783×
28,980×
30,175×
43,432×
41,296×
56,826×
38,896×
36,779×
33,171×
38,286×
34,248×
40,980×
39,413×
25,420×
29,824×
39,862×
36,829×
42,256×
45,727×
49,818×
66,569×
62,758×
60,119×
62,649×
79,279×
75,318×
55,731×
58,103×
39,237×
34,255×
55,883×
57,691×
41,353×
47,588×
49,361×
57,982×
48,801×
40,506×
29,625×
26,681×
40,172×
45,291×
40,232×
45,696×
35,552×
52,905×
38,695×
28,208×
31,015×
26,367×
31,114×
35,063×
22,472×
13,560×
14,896×
8,506×
965×
0s:
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27s:
28s:
0×
1×
33×
0×
0×
27,954×
73,814×
153,884×
231,814×
324,146×
381,554×
499,790×
663,150×
940,038×
1,217,332×
1,428,526×
1,603,536×
2,061,950×
2,203,386×
2,102,460×
1,953,640×
1,345,922×
757,898×
334,452×
157,688×
104,720×
43,760×
28,746×
3,366×
0s:
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114s:
0×
1×
3,113×
13,310×
22,290×
69,144×
130,417×
265,565×
239,796×
191,476×
257,071×
449,187×
566,495×
595,228×
627,986×
647,643×
691,960×
742,221×
817,675×
851,997×
901,131×
904,705×
978,979×
1,201,483×
1,367,845×
1,434,009×
1,524,121×
1,540,887×
1,596,353×
1,654,074×
1,451,590×
1,621,571×
1,745,832×
1,788,561×
1,697,636×
1,614,608×
1,362,070×
1,219,189×
1,366,038×
1,385,850×
1,384,785×
1,470,643×
1,404,420×
1,270,067×
1,151,084×
1,094,486×
1,371,981×
1,316,981×
1,428,669×
1,686,905×
1,919,386×
2,005,789×
1,742,913×
1,532,951×
1,597,911×
1,692,465×
1,770,446×
1,838,497×
1,688,645×
1,566,339×
1,553,965×
1,477,986×
1,586,222×
1,495,802×
1,413,027×
1,696,192×
1,591,013×
1,532,853×
1,252,466×
1,081,591×
746,021×
656,245×
818,009×
796,851×
810,851×
885,848×
991,510×
1,042,415×
872,022×
792,303×
854,129×
606,981×
633,037×
509,031×
371,570×
448,032×
340,266×
219,006×
222,686×
224,135×
205,950×
168,336×
147,524×
123,827×
102,492×
122,196×
52,307×
41,485×
18,670×
12,791×
9,718×
17,800×
26,367×
39,082×
71,038×
63,110×
103,386×
97,502×
68,670×
29,493×
13,462×
3,780×
6,861×
3,296×
2,567×
0s:
1s:
2s:
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47s:
0×
1×
48,065×
237,824×
576,692×
937,638×
1,773,144×
1,555,742×
2,094,930×
2,009,790×
2,263,678×
2,997,964×
4,736,380×
6,714,020×
5,694,406×
4,222,074×
1,877,872×
1,197,512×
357,036×
104,156×
27,608×
0×
0×
0×
532,974×
2,371,486×
5,605,528×
10,683,458×
20,719,154×
26,798,882×
33,499,684×
33,091,986×
33,081,400×
28,547,798×
26,351,278×
28,512,148×
28,830,294×
27,022,470×
22,198,370×
16,862,018×
13,512,244×
14,138,186×
13,254,830×
11,416,044×
6,882,548×
2,059,890×
405,654×
86,954×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
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170s:
171s:
0×
1×
3,113×
34,190×
110,898×
368,540×
1,224,913×
2,586,541×
2,913,709×
3,889,101×
5,284,852×
6,173,914×
7,562,359×
7,946,705×
8,120,561×
10,040,169×
10,902,966×
12,311,888×
10,642,999×
11,149,694×
13,785,262×
16,667,588×
18,390,094×
18,743,145×
16,709,448×
14,467,921×
16,004,683×
15,963,416×
16,459,718×
16,658,122×
14,025,002×
13,664,692×
13,215,303×
13,722,987×
11,640,582×
12,489,748×
14,936,849×
15,315,945×
18,377,051×
15,389,570×
15,635,231×
15,202,036×
15,500,651×
19,899,820×
24,140,733×
24,531,552×
28,637,642×
26,810,335×
26,426,596×
23,239,862×
22,603,623×
24,348,359×
22,037,891×
27,924,981×
28,793,165×
29,735,274×
29,788,201×
24,548,572×
25,808,645×
24,780,679×
23,905,087×
25,970,112×
21,964,878×
24,247,725×
25,938,677×
26,748,857×
23,809,771×
18,902,722×
19,580,345×
20,435,042×
28,034,108×
32,499,788×
26,900,427×
27,709,493×
26,213,757×
26,320,904×
26,034,046×
23,341,967×
28,514,300×
24,246,176×
20,563,909×
18,773,672×
16,584,680×
16,110,486×
17,572,493×
16,380,873×
16,595,870×
15,588,970×
15,676,902×
13,321,500×
12,954,299×
13,582,026×
12,262,031×
10,963,085×
14,638,452×
16,881,604×
14,837,408×
10,539,849×
8,511,583×
9,975,800×
9,542,150×
10,624,809×
10,470,938×
8,197,244×
8,937,721×
9,696,500×
8,155,118×
8,264,506×
8,221,369×
8,073,949×
6,335,710×
6,003,240×
5,261,966×
3,916,260×
5,805,397×
5,097,352×
5,862,159×
4,419,960×
2,820,405×
4,266,520×
4,423,081×
3,751,856×
3,668,055×
4,445,755×
4,431,387×
4,717,865×
3,754,846×
4,487,565×
3,340,500×
3,170,227×
3,253,669×
3,290,197×
2,254,752×
1,768,820×
2,010,902×
1,915,021×
3,072,801×
2,220,459×
1,443,129×
1,693,499×
2,182,434×
2,844,894×
2,165,920×
2,119,655×
1,623,489×
934,084×
1,839,102×
3,155,793×
3,192,380×
1,693,160×
1,322,463×
1,637,347×
1,526,474×
1,466,184×
1,107,862×
898,121×
916,307×
494,889×
260,607×
200,222×
92,296×
26,424×
120,258×
107,892×
38,068×
98,048×
128,904×
92,232×
5,616×
12,674×
16,412×
5,152×
0s:
1s:
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107s:
0×
1×
74,121×
705,358×
3,930,574×
8,067,280×
16,400,646×
29,836,504×
52,023,718×
59,375,098×
62,541,620×
50,546,666×
31,781,658×
22,266,012×
17,020,088×
12,670,760×
10,189,328×
12,608,288×
17,346,178×
15,829,618×
18,527,604×
20,657,824×
13,053,944×
9,933,730×
3,785,000×
994,802×
1,160,200×
774,928×
607,046×
235,130×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
3,260,294×
20,544,976×
57,082,720×
105,191,236×
171,566,548×
271,223,808×
335,318,238×
398,066,846×
393,176,974×
340,580,776×
315,064,712×
274,797,202×
284,628,788×
276,882,660×
279,901,698×
224,010,300×
164,404,580×
157,300,562×
159,690,778×
149,857,898×
124,379,402×
104,995,702×
98,945,094×
94,666,238×
102,890,670×
95,579,044×
114,463,442×
101,447,268×
124,464,780×
126,682,768×
169,329,994×
172,623,258×
169,832,028×
146,884,870×
126,988,090×
93,772,004×
91,019,584×
96,893,392×
106,542,832×
95,929,572×
71,529,406×
62,972,500×
47,749,392×
46,103,072×
40,377,020×
30,734,490×
16,909,368×
16,768,614×
15,049,748×
16,278,964×
17,506,202×
19,111,412×
24,103,580×
7,675,272×
2,137,258×
489,194×
18,290×