Base 38: 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
Average Steps
Full Cycle		1.97 step
avg		10.54 step
avg		9.73 step
avg		12.14 step
avg		13.07 step
avg		62.35 step
avg		18.06 step
avg		114.48 step
avg		20.12 step
avg		182.69 step
avg
Step Frequency
Full Cycle
0s:
1s:
2s:
0×
1×
37×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
0×
2×
61×
12×
0×
0×
3×
117×
102×
0×
0×
0×
6×
210×
228×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
0×
1×
417×
378×
754×
746×
734×
718×
698×
674×
646×
614×
578×
538×
494×
446×
394×
338×
278×
214×
146×
74×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
0×
1×
37×
0×
0×
0×
0×
0×
0×
0×
5,760×
14,328×
57,456×
11,112×
9,609×
1,791×
1,176×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
0×
1×
37×
1,100×
380×
9,412×
14,202×
15,932×
36,872×
54,124×
78,668×
87,424×
94,720×
77,268×
92,440×
83,174×
59,824×
49,140×
31,070×
23,984×
18,772×
13,380×
7,990×
754×
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:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
63s:
64s:
65s:
66s:
67s:
68s:
69s:
70s:
71s:
72s:
73s:
74s:
75s:
76s:
77s:
78s:
79s:
80s:
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:
0×
1×
417×
2,016×
4,050×
10,816×
7,958×
19,720×
40,116×
21,027×
13,966×
11,964×
23,342×
30,639×
28,237×
30,109×
33,220×
21,412×
25,612×
27,271×
38,325×
51,482×
55,942×
44,648×
51,131×
65,195×
78,601×
63,582×
53,912×
57,034×
57,055×
35,985×
32,703×
20,300×
22,838×
24,418×
8,611×
7,611×
11,120×
18,532×
11,346×
13,264×
19,276×
22,244×
26,670×
26,565×
34,038×
40,215×
27,778×
23,226×
20,224×
28,074×
39,058×
28,877×
23,289×
20,249×
7,394×
14,320×
63,585×
120,044×
128,026×
124,215×
147,829×
165,555×
161,058×
195,081×
175,541×
174,516×
148,374×
142,794×
172,633×
213,960×
228,925×
193,236×
178,621×
162,690×
147,379×
135,939×
121,414×
100,165×
98,307×
106,718×
94,607×
116,648×
75,385×
71,095×
62,380×
30,601×
25,423×
26,041×
35,400×
26,539×
30,986×
30,476×
19,536×
36,739×
29,996×
22,426×
24,876×
27,770×
21,074×
11,046×
11,019×
16,498×
6,296×
4,440×
3,806×
11,106×
7,204×
4,530×
4,130×
3,784×
4,144×
5,368×
9,724×
1,731×
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:
0×
1×
37×
0×
0×
42,510×
113,572×
223,046×
355,520×
354,768×
531,008×
864,788×
1,106,216×
1,539,328×
2,091,432×
2,485,286×
2,805,256×
3,295,654×
3,774,572×
3,721,404×
3,814,030×
3,553,292×
2,846,720×
1,879,962×
1,440,112×
858,050×
337,920×
203,508×
76,586×
4,710×
1,280×
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:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
63s:
64s:
65s:
66s:
67s:
68s:
69s:
70s:
71s:
72s:
73s:
74s:
75s:
76s:
77s:
78s:
79s:
80s:
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:
150s:
151s:
152s:
153s:
154s:
155s:
156s:
157s:
158s:
159s:
160s:
161s:
162s:
163s:
164s:
165s:
166s:
167s:
168s:
169s:
170s:
171s:
172s:
173s:
174s:
175s:
176s:
177s:
178s:
179s:
180s:
181s:
182s:
183s:
184s:
185s:
186s:
187s:
188s:
189s:
190s:
191s:
192s:
193s:
194s:
195s:
196s:
197s:
198s:
199s:
200s:
201s:
202s:
203s:
204s:
205s:
206s:
207s:
208s:
209s:
210s:
211s:
212s:
213s:
214s:
215s:
216s:
217s:
218s:
219s:
220s:
221s:
222s:
223s:
224s:
225s:
226s:
227s:
228s:
229s:
230s:
231s:
232s:
233s:
234s:
235s:
236s:
237s:
238s:
239s:
240s:
241s:
242s:
243s:
0×
1×
37×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
31,064×
108,168×
142,398×
304,207×
520,733×
296,340×
288,103×
232,376×
144,679×
178,711×
173,488×
227,455×
260,586×
285,149×
307,980×
308,188×
291,952×
235,866×
238,520×
110,434×
77,682×
79,089×
159,715×
118,193×
115,012×
76,091×
39,836×
16,146×
25,556×
39,643×
82,887×
31,934×
15,522×
35,751×
13,222×
140,666×
538,743×
714,420×
858,381×
1,049,769×
914,069×
984,951×
1,202,343×
1,221,585×
1,627,249×
1,788,950×
1,871,933×
1,606,718×
1,443,002×
1,412,220×
1,414,710×
1,479,589×
1,706,215×
1,688,071×
1,404,510×
1,313,542×
1,410,784×
1,466,858×
1,781,853×
1,647,399×
2,056,654×
1,820,382×
1,681,754×
1,677,587×
1,489,710×
1,603,760×
1,539,617×
1,547,984×
1,126,299×
1,139,403×
1,327,980×
1,336,496×
1,140,002×
1,161,836×
1,127,798×
802,446×
807,106×
858,065×
840,371×
872,277×
884,606×
1,243,920×
2,110,247×
1,902,523×
1,915,532×
1,731,515×
1,983,034×
1,830,296×
1,856,285×
1,868,807×
2,016,807×
2,477,785×
2,464,159×
2,355,346×
2,238,358×
2,412,933×
2,812,311×
2,646,644×
2,110,710×
2,230,973×
2,540,231×
2,102,208×
2,197,973×
2,179,486×
2,372,634×
2,318,888×
2,162,674×
2,256,769×
1,920,112×
2,016,394×
1,699,912×
1,925,561×
1,791,742×
1,871,896×
1,559,044×
1,451,849×
1,518,940×
1,875,822×
1,859,087×
1,968,891×
2,173,547×
2,076,555×
2,379,021×
2,339,634×
2,632,370×
2,053,869×
2,105,331×
1,996,972×
1,838,813×
1,433,509×
1,538,551×
1,698,523×
1,583,148×
1,212,348×
1,179,071×
1,036,628×
1,301,284×
1,305,148×
1,241,537×
1,165,852×
1,191,957×
1,099,133×
1,004,283×
980,279×
899,763×
1,050,570×
937,089×
811,467×
650,527×
648,707×
800,992×
802,212×
849,115×
830,112×
1,016,664×
826,709×
811,725×
684,999×
721,542×
818,293×
694,980×
691,461×
518,158×
647,075×
576,411×
479,791×
501,116×
563,117×
428,607×
439,958×
571,377×
646,295×
487,221×
528,751×
525,410×
510,960×
548,433×
648,838×
506,868×
385,512×
256,503×
330,068×
347,116×
338,915×
346,400×
321,862×
193,971×
289,382×
387,875×
408,703×
160,342×
128,122×
100,701×
125,643×
110,052×
122,459×
107,656×
93,394×
111,334×
129,423×
200,452×
171,699×
138,137×
83,902×
46,160×
62,675×
113,543×
90,330×
145,478×
136,752×
206,690×
203,131×
214,534×
148,669×
108,369×
99,596×
54,097×
99,896×
77,827×
89,489×
101,648×
166,300×
156,904×
145,589×
123,301×
106,786×
81,288×
71,096×
41,297×
59,152×
28,624×
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:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
0×
1×
39,841×
263,872×
732,696×
1,858,672×
4,827,334×
11,138,530×
18,310,918×
24,852,010×
31,502,836×
36,904,732×
49,244,610×
50,784,754×
52,072,658×
58,519,674×
55,621,650×
55,625,054×
50,837,750×
57,026,504×
63,069,410×
68,039,352×
62,526,016×
45,678,602×
33,973,882×
23,209,604×
27,763,022×
29,638,322×
30,739,862×
24,411,008×
20,843,562×
16,329,894×
11,388,174×
8,616,702×
7,862,368×
10,311,398×
13,843,914×
12,322,608×
4,848,508×
2,407,202×
1,506,068×
2,916,466×
4,166,816×
5,581,832×
4,477,272×
3,490,718×
1,028,904×
560,748×
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:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
63s:
64s:
65s:
66s:
67s:
68s:
69s:
70s:
71s:
72s:
73s:
74s:
75s:
76s:
77s:
78s:
79s:
80s:
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:
150s:
151s:
152s:
153s:
154s:
155s:
156s:
157s:
158s:
159s:
160s:
161s:
162s:
163s:
164s:
165s:
166s:
167s:
168s:
169s:
170s:
171s:
172s:
173s:
174s:
175s:
176s:
177s:
178s:
179s:
180s:
181s:
182s:
183s:
184s:
185s:
186s:
187s:
188s:
189s:
190s:
191s:
192s:
193s:
194s:
195s:
196s:
197s:
198s:
199s:
200s:
201s:
202s:
203s:
204s:
205s:
206s:
207s:
208s:
209s:
210s:
211s:
212s:
213s:
214s:
215s:
216s:
217s:
218s:
219s:
220s:
221s:
222s:
223s:
224s:
225s:
226s:
227s:
228s:
229s:
230s:
231s:
232s:
233s:
234s:
235s:
236s:
237s:
238s:
239s:
240s:
241s:
242s:
243s:
244s:
245s:
246s:
247s:
248s:
249s:
250s:
251s:
252s:
253s:
254s:
255s:
256s:
257s:
258s:
259s:
260s:
261s:
262s:
263s:
264s:
265s:
266s:
267s:
268s:
269s:
270s:
271s:
272s:
273s:
274s:
275s:
276s:
277s:
278s:
279s:
280s:
281s:
282s:
283s:
284s:
285s:
286s:
287s:
288s:
289s:
290s:
291s:
292s:
293s:
294s:
295s:
296s:
297s:
298s:
299s:
300s:
301s:
302s:
303s:
304s:
305s:
306s:
307s:
308s:
309s:
310s:
311s:
312s:
313s:
314s:
315s:
316s:
317s:
318s:
319s:
320s:
321s:
322s:
323s:
324s:
325s:
326s:
327s:
328s:
329s:
330s:
331s:
332s:
333s:
334s:
335s:
336s:
337s:
338s:
339s:
340s:
341s:
342s:
343s:
344s:
345s:
346s:
347s:
348s:
349s:
350s:
351s:
352s:
353s:
354s:
355s:
356s:
357s:
358s:
359s:
360s:
361s:
362s:
363s:
364s:
365s:
366s:
367s:
368s:
369s:
370s:
371s:
372s:
373s:
374s:
0×
1×
37×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
528,552×
4,247,620×
5,826,968×
6,749,645×
9,480,476×
10,921,070×
11,332,759×
11,236,168×
9,513,750×
9,144,129×
9,727,016×
9,092,919×
7,864,496×
9,862,824×
9,192,341×
14,584,183×
12,359,494×
14,470,035×
12,229,568×
12,105,007×
12,259,215×
13,706,342×
16,834,364×
19,083,220×
19,033,603×
18,035,708×
15,456,000×
15,772,726×
15,383,766×
14,721,394×
18,896,747×
18,222,060×
16,944,586×
19,508,638×
24,961,247×
25,526,627×
23,964,544×
19,045,915×
19,602,860×
23,917,454×
22,458,570×
24,549,594×
34,070,619×
39,644,914×
44,729,154×
44,936,985×
42,825,263×
39,036,725×
32,020,686×
34,966,550×
39,539,490×
47,398,508×
42,315,209×
40,439,836×
39,622,979×
41,329,938×
36,493,170×
32,913,313×
33,110,762×
35,565,530×
32,768,727×
31,003,503×
28,815,534×
34,370,454×
40,584,833×
35,434,392×
36,154,069×
36,201,146×
37,507,878×
36,206,700×
32,054,392×
31,841,271×
36,720,908×
35,398,232×
37,861,912×
33,295,756×
26,026,234×
25,991,528×
30,228,540×
33,014,058×
29,758,799×
28,904,625×
29,679,053×
36,790,403×
33,660,851×
33,017,168×
32,950,186×
35,642,143×
36,110,399×
35,803,307×
39,164,761×
38,490,143×
36,747,188×
31,476,435×
32,594,398×
35,523,475×
34,933,039×
30,565,105×
27,347,790×
27,175,440×
27,881,889×
26,533,632×
27,635,290×
30,558,267×
27,963,257×
27,361,491×
25,821,916×
22,803,943×
26,262,164×
32,280,913×
37,913,187×
34,649,828×
33,224,650×
33,689,002×
33,358,437×
39,149,119×
32,349,856×
27,168,327×
27,883,821×
27,062,596×
28,832,435×
31,824,569×
28,721,061×
26,077,347×
25,596,702×
27,485,226×
29,592,302×
29,856,490×
30,922,483×
31,998,179×
32,476,692×
31,817,614×
32,449,643×
32,350,479×
32,194,609×
32,604,778×
38,238,812×
38,510,412×
34,376,862×
31,830,488×
30,635,803×
27,348,807×
27,062,271×
28,838,274×
32,149,597×
30,279,560×
25,994,223×
21,614,844×
17,298,225×
17,016,000×
17,839,691×
20,042,850×
23,617,783×
20,342,835×
16,938,889×
15,630,614×
17,453,323×
18,772,863×
19,062,511×
17,451,765×
16,175,096×
13,541,370×
16,295,442×
16,865,539×
14,206,957×
14,972,656×
13,617,143×
12,801,913×
13,294,787×
11,375,828×
10,509,114×
12,045,093×
10,028,908×
12,546,967×
13,196,669×
14,618,062×
14,121,459×
12,973,829×
13,051,203×
10,356,982×
9,387,122×
8,681,376×
9,088,156×
10,014,210×
13,923,509×
13,130,245×
14,320,621×
16,077,031×
15,924,054×
13,677,940×
10,072,323×
11,244,293×
12,865,530×
15,377,474×
18,364,523×
16,060,475×
12,039,661×
10,841,085×
11,571,421×
7,568,522×
8,018,065×
7,402,458×
8,136,354×
8,841,927×
9,311,449×
9,830,473×
7,741,402×
6,623,662×
5,187,228×
4,053,450×
3,655,937×
3,276,251×
4,292,664×
3,888,398×
3,848,780×
3,716,311×
3,782,374×
2,687,273×
2,910,016×
2,742,042×
3,642,582×
4,258,864×
6,009,988×
4,995,022×
3,914,089×
2,671,166×
2,423,401×
2,153,199×
2,454,131×
3,830,921×
6,321,379×
5,182,570×
7,875,242×
9,538,346×
11,362,484×
7,815,091×
6,241,488×
5,611,499×
5,665,684×
6,204,125×
6,549,589×
6,612,327×
4,953,778×
4,317,442×
3,881,284×
3,465,262×
4,019,545×
3,460,111×
2,198,882×
2,546,598×
2,293,790×
2,423,314×
2,054,237×
1,694,195×
1,705,217×
2,615,661×
2,841,433×
3,295,949×
2,686,402×
2,064,387×
2,204,349×
2,118,099×
2,005,540×
1,563,695×
1,325,175×
3,581,569×
4,471,976×
2,568,108×
2,687,550×
1,875,329×
1,724,683×
1,497,649×
3,182,912×
3,026,852×
2,211,175×
1,752,427×
1,876,274×
1,840,298×
1,520,966×
1,917,785×
1,606,611×
557,765×
618,928×
500,229×
615,510×
478,775×
503,572×
673,387×
333,920×
632,570×
861,354×
2,059,536×
706,863×
410,787×
77,905×
4,708×
22,004×