Base 34: Iteration Frequencies: Cycle Start

Radix Character Encoding
0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V
W	X	Y	Z	a	b	c	d	e	f	g	h	i	j	k	l

Color Key
Orange	Fixed Point	number that becomes itself after one iteration
Green	Final Numbers	all numbers eventually reached, from all cycles
Purple	Cycle Start	iterations include entry into cycle, assuming it repeats
Red	Full Cycle	iterations include entire cycle, proving it repeats
Blue	Start Numbers	subset (optimization) of all numbers; minimal for full coverage
Gray	No Results	any calculation that has no results

Digits	1	2	3	4	5	6	7	8	9	10	11
Average Steps Cycle Start	0.97 step avg	1.44 step avg	7.97 step avg	3.20 step avg	7.96 step avg	27.92 step avg	12.89 step avg	42.10 step avg	11.20 step avg	51.90 step avg	19.08 step avg
Step Frequency Cycle Start	0s: 1s: 1× 33×	0s: 1s: 2s: 10× 313× 272×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 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: 1× 3,729× 9,016× 36,176× 7,903× 6,671× 1,449× 1,100×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 1× 12,767× 16,638× 11,674× 26,026× 43,102× 53,580× 53,510× 62,916× 60,758× 46,428× 48,810× 28,670× 20,700× 12,266× 4,096×	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: 1× 38,544× 88,377× 98,769× 60,733× 62,524× 84,593× 65,883× 62,697× 53,405× 57,254× 64,984× 51,632× 73,441× 53,210× 49,229× 49,455× 46,081× 43,771× 52,998× 49,773× 31,688× 37,006× 45,498× 49,115× 52,585× 62,127× 60,168× 73,171× 73,718× 70,289× 76,243× 88,218× 87,654× 72,427× 73,721× 64,579× 51,074× 68,137× 65,245× 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: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 1× 27,987× 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: 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: 1× 83,583× 298,639× 240,081× 228,711× 252,111× 374,639× 465,049× 451,772× 610,704× 715,894× 722,340× 779,591× 1,008,940× 1,065,637× 1,270,646× 1,147,753× 1,260,152× 1,254,082× 1,207,332× 1,252,507× 1,404,206× 1,573,789× 1,540,710× 1,539,154× 1,414,505× 1,425,581× 1,738,417× 1,725,276× 1,598,664× 1,639,473× 1,517,514× 1,461,492× 1,452,361× 1,364,560× 1,364,008× 1,665,007× 1,926,603× 1,795,064× 1,571,220× 1,434,690× 1,768,707× 1,611,856× 1,634,315× 1,752,610× 1,797,231× 1,690,479× 1,585,083× 1,630,779× 1,656,808× 1,662,607× 1,859,015× 1,764,118× 1,689,508× 1,447,695× 1,503,352× 1,431,844× 1,397,291× 1,350,120× 1,237,544× 1,270,342× 1,382,966× 1,223,380× 1,185,126× 1,033,412× 764,300× 749,739× 709,553× 684,179× 763,467× 730,806× 878,460× 830,086× 744,821× 761,877× 642,738× 468,972× 588,466× 466,749× 466,682× 425,150× 349,164× 245,531× 186,901× 120,390× 144,365× 230,014× 201,441× 125,617× 145,180× 169,917× 110,126× 159,450× 116,859× 79,027× 42,909× 19,473× 4,466× 6,861× 3,296× 2,567×	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: 1× 581,039× 2,609,310× 6,182,220× 11,621,096× 22,492,298× 28,354,624× 35,594,614× 35,101,776× 35,345,078× 31,545,762× 31,087,658× 35,226,168× 34,524,700× 31,244,544× 24,076,242× 18,059,530× 13,869,280× 14,242,342× 13,282,438× 11,416,044× 6,882,548× 2,059,890× 405,654× 86,954×	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: 1× 538,532× 3,985,358× 4,280,746× 7,736,894× 10,308,909× 11,143,842× 12,641,595× 11,297,139× 12,300,701× 14,079,791× 16,861,352× 17,349,949× 14,697,929× 15,754,807× 20,689,361× 25,514,126× 28,953,129× 25,854,633× 22,951,903× 21,771,225× 21,418,406× 21,041,226× 19,024,116× 19,671,060× 17,743,964× 18,083,648× 19,801,582× 18,626,449× 15,827,246× 15,475,028× 13,487,108× 12,825,153× 14,503,043× 16,492,188× 18,502,536× 18,464,099× 20,186,181× 20,693,496× 25,112,207× 28,962,221× 28,257,190× 26,041,881× 26,478,871× 24,750,597× 29,871,998× 32,037,960× 28,984,132× 30,685,920× 31,488,924× 32,813,523× 28,018,043× 26,755,501× 25,649,847× 25,820,660× 26,032,028× 22,704,699× 21,649,970× 21,372,644× 22,008,416× 26,371,246× 21,608,319× 20,503,445× 18,960,204× 17,211,197× 20,816,430× 20,942,273× 19,302,058× 19,032,868× 21,000,289× 23,538,748× 22,353,387× 22,309,542× 23,757,241× 21,423,773× 18,767,534× 17,877,875× 20,778,387× 19,380,346× 17,772,846× 15,726,873× 13,895,326× 13,512,792× 12,602,333× 12,427,890× 13,723,175× 15,013,931× 15,406,723× 12,639,931× 13,313,377× 13,191,724× 11,199,570× 8,766,931× 9,933,059× 11,494,400× 10,189,845× 10,553,469× 9,285,949× 7,996,819× 6,075,077× 6,336,197× 5,554,282× 6,247,202× 5,322,109× 6,170,432× 4,476,112× 4,444,733× 4,863,966× 4,120,410× 2,344,756× 2,032,150× 1,861,237× 1,442,144× 1,063,886× 770,659× 930,852× 787,182× 815,713× 1,134,837× 1,711,138× 1,532,378× 1,240,541× 1,988,435× 1,000,342× 1,186,721× 824,148× 1,053,832× 838,699× 1,049,969× 994,029× 806,540× 321,668× 395,714× 220,183× 269,455× 199,278× 228,387× 195,656× 134,282× 41,001× 38,998× 91,578× 109,553× 43,486× 106,364× 309,335× 895,098× 934,917× 627,027× 123,780× 133,457× 87,974× 102,634× 24,226× 5,457× 11,657× 5,102×	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: 1× 3,542,735× 22,764,910× 65,164,992× 120,396,610× 196,142,668× 309,671,160× 394,449,616× 468,533,324× 454,804,372× 378,847,392× 341,635,374× 292,197,674× 297,658,462× 290,270,358× 297,446,610× 240,409,944× 183,395,258× 178,070,402× 172,744,722× 159,791,628× 128,164,402× 105,990,504× 100,105,294× 95,441,166× 103,497,716× 95,814,174× 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×

Digits

Average Steps
Cycle Start

0.97 step
avg

1.44 step
avg

7.97 step
avg

3.20 step
avg

7.96 step
avg

27.92 step
avg

12.89 step
avg

42.10 step
avg

11.20 step
avg

51.90 step
avg

19.08 step
avg

Step Frequency
Cycle Start

0s:
1s:
1×
33×

0s:
1s:
2s:
10×
313×
272×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
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:
1×
3,729×
9,016×
36,176×
7,903×
6,671×
1,449×
1,100×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
1×
12,767×
16,638×
11,674×
26,026×
43,102×
53,580×
53,510×
62,916×
60,758×
46,428×
48,810×
28,670×
20,700×
12,266×
4,096×

0s:
1s:
2s:
3s:
4s:
5s:
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7s:
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9s:
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48s:
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50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
63s:
64s:
1×
38,544×
88,377×
98,769×
60,733×
62,524×
84,593×
65,883×
62,697×
53,405×
57,254×
64,984×
51,632×
73,441×
53,210×
49,229×
49,455×
46,081×
43,771×
52,998×
49,773×
31,688×
37,006×
45,498×
49,115×
52,585×
62,127×
60,168×
73,171×
73,718×
70,289×
76,243×
88,218×
87,654×
72,427×
73,721×
64,579×
51,074×
68,137×
65,245×
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:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
1×
27,987×
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:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
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17s:
18s:
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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:
1×
83,583×
298,639×
240,081×
228,711×
252,111×
374,639×
465,049×
451,772×
610,704×
715,894×
722,340×
779,591×
1,008,940×
1,065,637×
1,270,646×
1,147,753×
1,260,152×
1,254,082×
1,207,332×
1,252,507×
1,404,206×
1,573,789×
1,540,710×
1,539,154×
1,414,505×
1,425,581×
1,738,417×
1,725,276×
1,598,664×
1,639,473×
1,517,514×
1,461,492×
1,452,361×
1,364,560×
1,364,008×
1,665,007×
1,926,603×
1,795,064×
1,571,220×
1,434,690×
1,768,707×
1,611,856×
1,634,315×
1,752,610×
1,797,231×
1,690,479×
1,585,083×
1,630,779×
1,656,808×
1,662,607×
1,859,015×
1,764,118×
1,689,508×
1,447,695×
1,503,352×
1,431,844×
1,397,291×
1,350,120×
1,237,544×
1,270,342×
1,382,966×
1,223,380×
1,185,126×
1,033,412×
764,300×
749,739×
709,553×
684,179×
763,467×
730,806×
878,460×
830,086×
744,821×
761,877×
642,738×
468,972×
588,466×
466,749×
466,682×
425,150×
349,164×
245,531×
186,901×
120,390×
144,365×
230,014×
201,441×
125,617×
145,180×
169,917×
110,126×
159,450×
116,859×
79,027×
42,909×
19,473×
4,466×
6,861×
3,296×
2,567×

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:
1×
581,039×
2,609,310×
6,182,220×
11,621,096×
22,492,298×
28,354,624×
35,594,614×
35,101,776×
35,345,078×
31,545,762×
31,087,658×
35,226,168×
34,524,700×
31,244,544×
24,076,242×
18,059,530×
13,869,280×
14,242,342×
13,282,438×
11,416,044×
6,882,548×
2,059,890×
405,654×
86,954×

0s:
1s:
2s:
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150s:
151s:
152s:
153s:
154s:
155s:
156s:
1×
538,532×
3,985,358×
4,280,746×
7,736,894×
10,308,909×
11,143,842×
12,641,595×
11,297,139×
12,300,701×
14,079,791×
16,861,352×
17,349,949×
14,697,929×
15,754,807×
20,689,361×
25,514,126×
28,953,129×
25,854,633×
22,951,903×
21,771,225×
21,418,406×
21,041,226×
19,024,116×
19,671,060×
17,743,964×
18,083,648×
19,801,582×
18,626,449×
15,827,246×
15,475,028×
13,487,108×
12,825,153×
14,503,043×
16,492,188×
18,502,536×
18,464,099×
20,186,181×
20,693,496×
25,112,207×
28,962,221×
28,257,190×
26,041,881×
26,478,871×
24,750,597×
29,871,998×
32,037,960×
28,984,132×
30,685,920×
31,488,924×
32,813,523×
28,018,043×
26,755,501×
25,649,847×
25,820,660×
26,032,028×
22,704,699×
21,649,970×
21,372,644×
22,008,416×
26,371,246×
21,608,319×
20,503,445×
18,960,204×
17,211,197×
20,816,430×
20,942,273×
19,302,058×
19,032,868×
21,000,289×
23,538,748×
22,353,387×
22,309,542×
23,757,241×
21,423,773×
18,767,534×
17,877,875×
20,778,387×
19,380,346×
17,772,846×
15,726,873×
13,895,326×
13,512,792×
12,602,333×
12,427,890×
13,723,175×
15,013,931×
15,406,723×
12,639,931×
13,313,377×
13,191,724×
11,199,570×
8,766,931×
9,933,059×
11,494,400×
10,189,845×
10,553,469×
9,285,949×
7,996,819×
6,075,077×
6,336,197×
5,554,282×
6,247,202×
5,322,109×
6,170,432×
4,476,112×
4,444,733×
4,863,966×
4,120,410×
2,344,756×
2,032,150×
1,861,237×
1,442,144×
1,063,886×
770,659×
930,852×
787,182×
815,713×
1,134,837×
1,711,138×
1,532,378×
1,240,541×
1,988,435×
1,000,342×
1,186,721×
824,148×
1,053,832×
838,699×
1,049,969×
994,029×
806,540×
321,668×
395,714×
220,183×
269,455×
199,278×
228,387×
195,656×
134,282×
41,001×
38,998×
91,578×
109,553×
43,486×
106,364×
309,335×
895,098×
934,917×
627,027×
123,780×
133,457×
87,974×
102,634×
24,226×
5,457×
11,657×
5,102×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
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8s:
9s:
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44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
1×
3,542,735×
22,764,910×
65,164,992×
120,396,610×
196,142,668×
309,671,160×
394,449,616×
468,533,324×
454,804,372×
378,847,392×
341,635,374×
292,197,674×
297,658,462×
290,270,358×
297,446,610×
240,409,944×
183,395,258×
178,070,402×
172,744,722×
159,791,628×
128,164,402×
105,990,504×
100,105,294×
95,441,166×
103,497,716×
95,814,174×
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×