Base 7: Summary: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets] — [2] [3] [4] [5] [6] [Base 7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144] [145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168] [169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179] [180] [181] [182] [183] [184] [185] [186] [187] [188] [189] [190] [191] [192] [193] [194] [195] [196] [197] [198] [199] [200] [201] [202] [203] [204] [205] [206] [207] [208] [209] [210] [211] [212] [213] [214] [215] [216] [217] [218] [219] [220] [221] [222] [223] [224] [225] [226] [227] [228] [229] [230] [231] [232] [233] [234] [235] [236] [237] [238] [239] [240] [241] [242] [243] [244] [245] [246] [247] [248] [249] [250] [251] [252] [253] [254] [255]
[Odd Digit Sets]
[Even Digit Sets]
Final Numbers
[Fixed Points]
Cycles Lengths
[All Digit Sets]
[Odd Digit Sets]
[Even Digit Sets]
Iteration Frequencies
[Cycle Start]
[Full Cycle]
Maximum Iteration Sequences
[Cycle Start]
[Full Cycle]
Cycles Sequences
[Maximum Length Cycle Count]
[All Cycle Counts]

Radix Character Encoding
0	1	2	3	4	5	6

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	# Start Numbers	# Fixed Points (excluding zero)	# Cycles (including fixed) (excluding zero)	Full Cycle Max Length	Avg Steps including Cycle Start	Max Steps including Cycle Start	Avg Steps including Full Cycle	Max Steps including Full Cycle	# Final Numbers (excluding zero)
1	7	0 fixed pts	0 cycles	0 nodes	0.86 avg steps	1 max steps	1.86 avg steps	2 max steps	0 final numbers
2	28	0 fixed pts	0 cycles	0 nodes	2.79 avg steps	4 max steps	3.79 avg steps	5 max steps	0 final numbers
3	84	0 fixed pts	1 cycle	2 nodes	2.08 avg steps	4 max steps	4.00 avg steps	6 max steps	2 final numbers
4	210	0 fixed pts	1 cycle	3 nodes	2.36 avg steps	4 max steps	5.29 avg steps	7 max steps	3 final numbers
5	462	0 fixed pts	1 cycle	5 nodes	2.93 avg steps	6 max steps	7.87 avg steps	11 max steps	5 final numbers
6	924	0 fixed pts	1 cycle	6 nodes	3.31 avg steps	7 max steps	9.27 avg steps	13 max steps	6 final numbers
7	1,716	0 fixed pts	1 cycle	6 nodes	6.25 avg steps	14 max steps	12.23 avg steps	20 max steps	6 final numbers
8	3,003	0 fixed pts	1 cycle	6 nodes	4.37 avg steps	9 max steps	10.36 avg steps	15 max steps	6 final numbers
9	5,005	0 fixed pts	1 cycle	11 nodes	7.58 avg steps	15 max steps	18.57 avg steps	26 max steps	11 final numbers
10	8,008	0 fixed pts	3 cycles	2 nodes	5.46 avg steps	11 max steps	7.46 avg steps	13 max steps	6 final numbers
11	12,376	1 fixed pt	1 cycle	1 node	8.35 avg steps	17 max steps	9.35 avg steps	18 max steps	1 final number
12	18,564	0 fixed pts	2 cycles	5 nodes	6.97 avg steps	16 max steps	11.34 avg steps	21 max steps	7 final numbers
13	27,132	2 fixed pts	3 cycles	6 nodes	5.94 avg steps	14 max steps	10.65 avg steps	20 max steps	8 final numbers
14	38,760	0 fixed pts	2 cycles	9 nodes	6.36 avg steps	16 max steps	11.84 avg steps	21 max steps	11 final numbers
15	54,264	3 fixed pts	4 cycles	2 nodes	7.02 avg steps	15 max steps	8.48 avg steps	17 max steps	5 final numbers
16	74,613	0 fixed pts	2 cycles	12 nodes	7.38 avg steps	23 max steps	13.40 avg steps	25 max steps	14 final numbers
17	100,947	4 fixed pts	5 cycles	2 nodes	7.96 avg steps	21 max steps	9.30 avg steps	22 max steps	6 final numbers
18	134,596	0 fixed pts	1 cycle	2 nodes	11.20 avg steps	23 max steps	13.20 avg steps	25 max steps	2 final numbers
19	177,100	5 fixed pts	8 cycles	4 nodes	6.29 avg steps	17 max steps	8.50 avg steps	21 max steps	13 final numbers
20	230,230	1 fixed pt	6 cycles	7 nodes	6.54 avg steps	17 max steps	10.75 avg steps	21 max steps	19 final numbers
21	296,010	6 fixed pts	10 cycles	3 nodes	7.48 avg steps	23 max steps	9.61 avg steps	26 max steps	15 final numbers
22	376,740	2 fixed pts	5 cycles	5 nodes	10.03 avg steps	29 max steps	14.24 avg steps	34 max steps	11 final numbers
23	475,020	7 fixed pts	13 cycles	3 nodes	7.77 avg steps	28 max steps	9.86 avg steps	31 max steps	21 final numbers
24	593,775	3 fixed pts	7 cycles	5 nodes	8.49 avg steps	23 max steps	12.74 avg steps	28 max steps	17 final numbers
25	736,281	8 fixed pts	18 cycles	3 nodes	8.12 avg steps	33 max steps	9.83 avg steps	34 max steps	31 final numbers
26	906,192	4 fixed pts	7 cycles	24 nodes	6.70 avg steps	21 max steps	26.33 avg steps	44 max steps	32 final numbers
27	1,107,568	9 fixed pts	20 cycles	3 nodes	7.80 avg steps	34 max steps	10.10 avg steps	37 max steps	35 final numbers
28	1,344,904	5 fixed pts	8 cycles	7 nodes	10.92 avg steps	31 max steps	16.61 avg steps	38 max steps	16 final numbers
29	1,623,160	11 fixed pts	25 cycles	3 nodes	6.42 avg steps	31 max steps	8.70 avg steps	34 max steps	45 final numbers
30	1,947,792	6 fixed pts	12 cycles	25 nodes	7.14 avg steps	25 max steps	26.30 avg steps	50 max steps	42 final numbers
31	2,324,784	13 fixed pts	30 cycles	3 nodes	6.50 avg steps	33 max steps	8.85 avg steps	36 max steps	55 final numbers
32	2,760,681	7 fixed pts	13 cycles	13 nodes	9.64 avg steps	32 max steps	18.44 avg steps	45 max steps	31 final numbers
33	3,262,623	15 fixed pts	35 cycles	3 nodes	6.53 avg steps	35 max steps	8.89 avg steps	38 max steps	65 final numbers
34	3,838,380	8 fixed pts	15 cycles	13 nodes	9.70 avg steps	30 max steps	19.35 avg steps	43 max steps	34 final numbers
35	4,496,388	17 fixed pts	43 cycles	5 nodes	6.26 avg steps	37 max steps	8.86 avg steps	40 max steps	84 final numbers
36	5,245,786	9 fixed pts	16 cycles	3 nodes	17.33 avg steps	51 max steps	18.64 avg steps	52 max steps	24 final numbers
37	6,096,454	19 fixed pts	51 cycles	5 nodes	6.01 avg steps	39 max steps	8.74 avg steps	42 max steps	107 final numbers
38	7,059,052	11 fixed pts	20 cycles	17 nodes	9.31 avg steps	36 max steps	19.13 avg steps	53 max steps	45 final numbers
39	8,145,060	21 fixed pts	56 cycles	5 nodes	6.14 avg steps	41 max steps	9.01 avg steps	44 max steps	117 final numbers
40	9,366,819	13 fixed pts	25 cycles	3 nodes	14.24 avg steps	46 max steps	16.50 avg steps	49 max steps	39 final numbers
41	10,737,573	23 fixed pts	63 cycles	6 nodes	5.86 avg steps	43 max steps	8.98 avg steps	46 max steps	138 final numbers
42	12,271,512	15 fixed pts	29 cycles	11 nodes	13.39 avg steps	53 max steps	19.14 avg steps	64 max steps	54 final numbers
43	13,983,816	25 fixed pts	71 cycles	6 nodes	5.79 avg steps	45 max steps	9.08 avg steps	48 max steps	164 final numbers
44	15,890,700	17 fixed pts	33 cycles	3 nodes	12.73 avg steps	52 max steps	15.01 avg steps	55 max steps	53 final numbers
45	18,009,460	27 fixed pts	79 cycles	6 nodes	5.88 avg steps	47 max steps	9.35 avg steps	50 max steps	184 final numbers
46	20,358,520	19 fixed pts	38 cycles	7 nodes	12.00 avg steps	50 max steps	14.60 avg steps	53 max steps	67 final numbers
47	22,957,480	30 fixed pts	89 cycles	6 nodes	5.69 avg steps	49 max steps	9.10 avg steps	52 max steps	212 final numbers
48	25,827,165	21 fixed pts	42 cycles	3 nodes	11.98 avg steps	57 max steps	14.13 avg steps	60 max steps	70 final numbers
49	28,989,675	33 fixed pts	99 cycles	6 nodes	5.71 avg steps	51 max steps	9.20 avg steps	54 max steps	240 final numbers
50	32,468,436	23 fixed pts	48 cycles	3 nodes	13.51 avg steps	56 max steps	15.77 avg steps	59 max steps	81 final numbers
51	36,288,252	36 fixed pts	112 cycles	6 nodes	5.67 avg steps	53 max steps	9.08 avg steps	56 max steps	277 final numbers
52	40,475,358	25 fixed pts	53 cycles	3 nodes	11.44 avg steps	54 max steps	13.67 avg steps	57 max steps	90 final numbers
53	45,057,474	39 fixed pts	123 cycles	6 nodes	5.56 avg steps	55 max steps	9.12 avg steps	58 max steps	310 final numbers
54	50,063,860	27 fixed pts	57 cycles	3 nodes	13.18 avg steps	61 max steps	15.50 avg steps	64 max steps	97 final numbers
55	55,525,372	42 fixed pts	137 cycles	6 nodes	5.60 avg steps	57 max steps	9.18 avg steps	60 max steps	350 final numbers
56	61,474,519	30 fixed pts	63 cycles	3 nodes	12.49 avg steps	60 max steps	14.47 avg steps	63 max steps	108 final numbers
57	67,945,521	45 fixed pts	150 cycles	6 nodes	5.56 avg steps	59 max steps	9.18 avg steps	62 max steps	388 final numbers
58	74,974,368	33 fixed pts	71 cycles	3 nodes	11.31 avg steps	58 max steps	13.57 avg steps	61 max steps	125 final numbers
59	82,598,880	48 fixed pts	164 cycles	9 nodes	5.45 avg steps	61 max steps	9.25 avg steps	64 max steps	436 final numbers
60	90,858,768	36 fixed pts	79 cycles	3 nodes	11.54 avg steps	65 max steps	13.88 avg steps	68 max steps	140 final numbers
61	99,795,696	51 fixed pts	177 cycles	9 nodes	5.47 avg steps	63 max steps	9.39 avg steps	66 max steps	481 final numbers
62	109,453,344	39 fixed pts	87 cycles	3 nodes	10.98 avg steps	64 max steps	13.14 avg steps	67 max steps	155 final numbers
63	119,877,472	54 fixed pts	190 cycles	9 nodes	5.43 avg steps	65 max steps	9.52 avg steps	68 max steps	526 final numbers
64	131,115,985	42 fixed pts	95 cycles	11 nodes	10.35 avg steps	62 max steps	12.97 avg steps	65 max steps	179 final numbers
65	143,218,999	58 fixed pts	210 cycles	9 nodes	5.37 avg steps	67 max steps	9.49 avg steps	70 max steps	591 final numbers
66	156,238,908	45 fixed pts	101 cycles	3 nodes	10.85 avg steps	69 max steps	13.00 avg steps	72 max steps	181 final numbers
67	170,230,452	62 fixed pts	229 cycles	9 nodes	5.34 avg steps	69 max steps	9.56 avg steps	72 max steps	653 final numbers
68	185,250,786	48 fixed pts	109 cycles	5 nodes	10.27 avg steps	68 max steps	12.60 avg steps	71 max steps	199 final numbers
69	201,359,550	66 fixed pts	246 cycles	9 nodes	5.34 avg steps	71 max steps	9.58 avg steps	74 max steps	713 final numbers
70	218,618,940	51 fixed pts	119 cycles	5 nodes	10.29 avg steps	66 max steps	12.60 avg steps	69 max steps	221 final numbers
71	237,093,780	70 fixed pts	263 cycles	11 nodes	5.30 avg steps	73 max steps	9.80 avg steps	76 max steps	779 final numbers
72	256,851,595	54 fixed pts	132 cycles	5 nodes	9.89 avg steps	73 max steps	12.44 avg steps	76 max steps	252 final numbers
73	277,962,685	74 fixed pts	280 cycles	11 nodes	5.30 avg steps	75 max steps	9.92 avg steps	78 max steps	845 final numbers
74	300,500,200	58 fixed pts	141 cycles	5 nodes	9.74 avg steps	72 max steps	12.14 avg steps	75 max steps	271 final numbers
75	324,540,216	78 fixed pts	300 cycles	11 nodes	5.29 avg steps	77 max steps	10.06 avg steps	80 max steps	918 final numbers
76	350,161,812	62 fixed pts	151 cycles	9 nodes	9.29 avg steps	70 max steps	11.80 avg steps	73 max steps	299 final numbers
77	377,447,148	82 fixed pts	321 cycles	11 nodes	5.23 avg steps	79 max steps	10.09 avg steps	82 max steps	1,000 final numbers
78	406,481,544	66 fixed pts	161 cycles	5 nodes	9.25 avg steps	77 max steps	11.65 avg steps	80 max steps	317 final numbers
79	437,353,560	86 fixed pts	343 cycles	11 nodes	5.21 avg steps	81 max steps	10.27 avg steps	84 max steps	1,087 final numbers
80	470,155,077	70 fixed pts	172 cycles	6 nodes	8.99 avg steps	76 max steps	11.51 avg steps	79 max steps	341 final numbers
81	504,981,379	90 fixed pts	362 cycles	11 nodes	5.24 avg steps	83 max steps	10.41 avg steps	86 max steps	1,165 final numbers
82	541,931,236	74 fixed pts	185 cycles	6 nodes	8.91 avg steps	74 max steps	11.38 avg steps	77 max steps	372 final numbers
83	581,106,988	95 fixed pts	384 cycles	11 nodes	5.21 avg steps	85 max steps	10.52 avg steps	88 max steps	1,256 final numbers
84	622,614,630	78 fixed pts	195 cycles	6 nodes	8.82 avg steps	81 max steps	11.44 avg steps	84 max steps	397 final numbers
85	666,563,898	100 fixed pts	408 cycles	11 nodes	5.20 avg steps	87 max steps	10.60 avg steps	90 max steps	1,351 final numbers
86	713,068,356	82 fixed pts	210 cycles	6 nodes	8.53 avg steps	80 max steps	11.13 avg steps	83 max steps	437 final numbers
87	762,245,484	105 fixed pts	433 cycles	11 nodes	5.19 avg steps	89 max steps	10.68 avg steps	92 max steps	1,448 final numbers
88	814,216,767	86 fixed pts	221 cycles	6 nodes	8.41 avg steps	78 max steps	11.11 avg steps	81 max steps	465 final numbers
89	869,107,785	110 fixed pts	456 cycles	14 nodes	5.15 avg steps	91 max steps	10.84 avg steps	94 max steps	1,553 final numbers
90	927,048,304	90 fixed pts	234 cycles	6 nodes	8.41 avg steps	85 max steps	11.06 avg steps	88 max steps	497 final numbers
91	988,172,368	115 fixed pts	479 cycles	14 nodes	5.15 avg steps	93 max steps	10.99 avg steps	96 max steps	1,658 final numbers
92	1,052,618,392	95 fixed pts	251 cycles	6 nodes	8.16 avg steps	84 max steps	10.88 avg steps	87 max steps	538 final numbers
93	1,120,529,256	120 fixed pts	506 cycles	14 nodes	5.16 avg steps	95 max steps	11.18 avg steps	98 max steps	1,775 final numbers
94	1,192,052,400	100 fixed pts	266 cycles	6 nodes	8.08 avg steps	82 max steps	10.77 avg steps	85 max steps	576 final numbers
95	1,267,339,920	125 fixed pts	534 cycles	14 nodes	5.13 avg steps	97 max steps	11.20 avg steps	100 max steps	1,899 final numbers
96	1,346,548,665	105 fixed pts	280 cycles	6 nodes	8.08 avg steps	89 max steps	10.85 avg steps	92 max steps	611 final numbers
97	1,429,840,335	130 fixed pts	565 cycles	14 nodes	5.11 avg steps	99 max steps	11.29 avg steps	102 max steps	2,030 final numbers
98	1,517,381,580	110 fixed pts	294 cycles	6 nodes	8.24 avg steps	88 max steps	10.95 avg steps	91 max steps	646 final numbers
99	1,609,344,100	135 fixed pts	591 cycles	14 nodes	5.12 avg steps	101 max steps	11.34 avg steps	104 max steps	2,150 final numbers
100	1,705,904,746	115 fixed pts	315 cycles	11 nodes	7.84 avg steps	86 max steps	10.79 avg steps	89 max steps	708 final numbers