Base 46: 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
Average Steps
Full Cycle
1.98 step
avg
23.52 step
avg
11.24 step
avg
14.06 step
avg
13.55 step
avg
124.87 step
avg
18.98 step
avg
258.83 step
avg
24.19 step
avg
Step Frequency
Full Cycle
0s:
1s:
2s:


45×
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:


45×




















12×
517×
506×
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:


597×
550×
1,098×
1,090×
1,078×
1,062×
1,042×
1,018×
990×
958×
922×
882×
838×
790×
738×
682×
622×
558×
490×
418×
342×
262×
178×
90×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:


45×









12,320×
31,570×
126,500×
19,890×
17,273×
2,583×
1,694×
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:


45×
1,608×
12,654×
31,762×
29,722×
39,738×
76,680×
88,906×
146,768×
168,322×
219,406×
201,106×
246,624×
193,710×
208,716×
135,804×
134,640×
86,076×
54,580×
29,904×
10,534×
1,364×
90×
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:


597×



























































62,525×
181,783×
179,133×
175,373×
211,396×
197,621×
165,514×
126,566×
147,979×
130,702×
135,092×
119,134×
121,446×
133,480×
145,182×
150,941×
196,346×
188,315×
209,361×
173,617×
172,712×
189,880×
155,400×
173,484×
163,174×
134,695×
130,450×
173,521×
179,993×
150,376×
155,369×
163,241×
150,672×
106,160×
115,253×
93,530×
100,367×
83,657×
101,053×
118,072×
101,772×
123,293×
132,626×
111,109×
94,927×
149,458×
84,326×
130,475×
145,417×
198,400×
194,566×
201,716×
197,821×
165,979×
158,895×
195,977×
208,894×
188,965×
191,451×
264,513×
257,508×
252,840×
249,194×
232,095×
182,655×
175,242×
187,795×
157,705×
128,810×
172,237×
138,762×
98,907×
134,022×
145,598×
159,691×
152,725×
119,895×
120,232×
94,378×
91,645×
129,680×
82,660×
68,623×
69,333×
95,288×
110,966×
88,751×
79,229×
125,637×
100,309×
141,173×
158,470×
107,665×
81,118×
73,873×
88,922×
86,081×
76,551×
66,519×
62,224×
48,185×
59,190×
63,782×
56,523×
41,415×
46,312×
64,181×
59,045×
68,100×
60,370×
86,718×
39,265×
57,597×
39,716×
55,463×
64,292×
95,346×
80,145×
62,823×
78,173×
38,184×
64,534×
47,987×
55,502×
61,786×
51,405×
63,325×
75,549×
64,626×
101,505×
97,306×
64,965×
80,044×
83,426×
67,205×
67,139×
112,012×
109,862×
123,973×
103,890×
131,521×
127,966×
124,170×
118,198×
44,912×
35,266×
45,522×
22,334×
23,194×
10,012×
13,578×
6,162×
13,099×
14,661×
20,008×
24,702×
19,184×
15,154×
20,782×
21,824×
32,986×
12,758×
1,850×
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:


45×


87,708×
235,454×
465,860×
740,904×
1,019,514×
1,570,820×
2,494,374×
3,276,076×
4,647,004×
6,147,476×
7,127,800×
7,577,732×
8,420,134×
9,711,720×
11,874,910×
13,495,976×
15,021,564×
12,997,070×
11,129,604×
7,613,214×
4,859,518×
1,845,106×
759,284×
424,798×
153,638×
58,116×
22,468×
6,672×
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:
375s:
376s:
377s:
378s:
379s:
380s:
381s:
382s:
383s:
384s:
385s:
386s:
387s:
388s:
389s:
390s:
391s:
392s:
393s:
394s:
395s:
396s:
397s:
398s:
399s:
400s:
401s:
402s:
403s:
404s:


45×




















































291,267×
1,214,993×
1,254,632×
2,022,560×
2,274,951×
2,150,882×
1,877,197×
1,624,229×
2,100,914×
2,081,174×
1,510,108×
1,776,007×
2,176,304×
2,493,662×
2,250,767×
2,660,729×
2,345,145×
2,370,000×
2,503,873×
2,337,615×
2,131,510×
2,394,456×
2,561,351×
3,171,094×
3,066,753×
2,693,848×
2,060,802×
2,049,937×
1,755,736×
1,955,314×
2,094,081×
2,288,394×
2,364,981×
2,344,162×
2,746,579×
2,972,997×
3,206,069×
3,595,987×
2,786,895×
2,526,677×
2,416,717×
2,359,794×
2,356,972×
1,856,014×
1,803,468×
1,839,561×
1,542,968×
1,577,275×
1,725,661×
1,255,395×
1,369,389×
1,721,915×
2,501,042×
2,492,756×
2,059,031×
2,341,876×
1,547,874×
1,167,621×
1,098,814×
892,556×
1,156,138×
1,324,122×
1,124,911×
1,033,948×
1,026,751×
910,318×
820,042×
772,693×
664,896×
501,509×
379,411×
178,285×
239,186×
231,361×
225,861×
227,932×
316,174×
276,841×
187,854×
260,393×
69,680×
100,364×
63,971×







































































































1,253,941×
6,120,509×
6,479,307×
7,985,535×
8,794,906×
9,128,203×
9,447,371×
9,640,751×
9,857,366×
10,463,913×
9,710,247×
9,198,035×
9,182,187×
9,609,972×
10,157,587×
9,680,284×
8,964,934×
9,456,974×
9,939,400×
9,687,424×
10,220,912×
10,187,338×
10,574,390×
10,026,034×
8,628,032×
10,016,361×
10,529,411×
8,333,982×
8,782,816×
9,659,983×
8,692,252×
8,483,199×
7,854,211×
8,978,066×
10,406,288×
11,583,082×
10,775,643×
10,490,724×
8,818,554×
7,787,495×
7,682,578×
8,078,023×
8,740,745×
8,143,559×
7,059,256×
6,132,626×
6,183,923×
5,777,534×
6,406,417×
5,673,505×
4,827,108×
4,475,695×
4,297,695×
3,838,403×
3,592,820×
4,044,526×
4,340,769×
4,749,619×
4,361,350×
4,795,408×
4,394,448×
4,656,377×
5,240,350×
5,336,821×
4,773,366×
4,625,298×
5,089,384×
5,284,557×
5,456,746×
4,387,150×
3,520,424×
4,156,145×
4,416,803×
4,902,581×
4,743,853×
4,687,184×
4,297,460×
5,066,329×
5,833,456×
4,890,698×
5,278,121×
6,144,355×
5,757,245×
5,734,954×
5,654,983×
5,230,141×
5,135,601×
5,623,889×
5,702,385×
4,803,651×
4,780,536×
4,822,101×
4,783,615×
4,123,773×
4,098,975×
4,210,976×
4,064,872×
3,183,315×
3,677,568×
3,619,419×
3,859,111×
4,361,774×
4,202,791×
3,831,819×
3,134,796×
2,503,319×
2,239,440×
2,759,309×
2,823,098×
2,911,869×
2,842,289×
2,801,204×
2,921,676×
3,146,592×
1,892,994×
1,611,186×
1,152,499×
1,197,084×
1,200,383×
1,238,583×
1,129,462×
1,185,151×
1,186,638×
1,070,677×
607,340×
785,570×
798,704×
920,640×
796,111×
831,510×
718,336×
916,379×
1,079,512×
1,341,772×
1,221,070×
1,054,116×
1,047,329×
898,036×
1,021,961×
782,991×
593,855×
548,372×
503,809×
373,306×
571,270×
590,709×
219,263×
227,597×
360,867×
191,612×
97,950×
93,554×
164,606×
282,528×
121,931×
75,562×
51,000×
60,617×
26,335×
11,237×
14,196×
25,800×
5,597×
2,915×
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:


187,077×
1,287,682×
3,760,278×
7,473,836×
13,985,968×
26,502,652×
43,083,044×
62,847,108×
76,074,888×
82,517,388×
75,905,646×
91,057,752×
97,407,010×
135,950,640×
169,513,236×
210,301,588×
248,617,316×
261,460,590×
237,221,028×
227,123,940×
195,701,112×
228,697,174×
229,632,444×
232,754,028×
238,753,864×
243,959,810×
249,317,462×
236,724,168×
164,174,490×
157,657,324×
131,854,810×
166,522,186×
166,338,656×
192,314,616×
147,243,144×
92,744,956×
63,670,640×
34,889,954×
27,683,416×
16,436,128×
9,580,708×
8,451,522×
5,187,892×
4,398,878×
922,722×
24,558×
20,930×