Base 4: Summary: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets] — [2] [3] [Base 4] [5] [6] [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

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	4	0 fixed pts	0 cycles	0 nodes	0.75 avg steps	1 max steps	1.75 avg steps	2 max steps	0 final numbers
2	10	0 fixed pts	1 cycle	2 nodes	1.00 avg steps	2 max steps	2.60 avg steps	4 max steps	2 final numbers
3	20	1 fixed pt	1 cycle	1 node	1.75 avg steps	3 max steps	2.75 avg steps	4 max steps	1 final number
4	35	1 fixed pt	2 cycles	2 nodes	1.71 avg steps	3 max steps	3.34 avg steps	5 max steps	3 final numbers
5	56	0 fixed pts	1 cycle	2 nodes	2.38 avg steps	4 max steps	4.30 avg steps	6 max steps	2 final numbers
6	84	3 fixed pts	3 cycles	1 node	3.42 avg steps	6 max steps	4.42 avg steps	7 max steps	3 final numbers
7	120	1 fixed pt	1 cycle	1 node	3.34 avg steps	6 max steps	4.34 avg steps	7 max steps	1 final number
8	165	3 fixed pts	4 cycles	3 nodes	3.14 avg steps	6 max steps	5.35 avg steps	9 max steps	6 final numbers
9	220	3 fixed pts	3 cycles	1 node	3.37 avg steps	6 max steps	4.37 avg steps	7 max steps	3 final numbers
10	286	5 fixed pts	5 cycles	1 node	3.57 avg steps	7 max steps	4.57 avg steps	8 max steps	5 final numbers
11	364	3 fixed pts	4 cycles	3 nodes	2.59 avg steps	5 max steps	4.51 avg steps	7 max steps	6 final numbers
12	455	8 fixed pts	8 cycles	1 node	3.35 avg steps	7 max steps	4.35 avg steps	8 max steps	8 final numbers
13	560	5 fixed pts	5 cycles	1 node	3.10 avg steps	6 max steps	4.10 avg steps	7 max steps	5 final numbers
14	680	9 fixed pts	10 cycles	3 nodes	2.88 avg steps	6 max steps	4.59 avg steps	9 max steps	12 final numbers
15	816	8 fixed pts	8 cycles	1 node	3.09 avg steps	6 max steps	4.09 avg steps	7 max steps	8 final numbers
16	969	12 fixed pts	12 cycles	1 node	3.09 avg steps	6 max steps	4.09 avg steps	7 max steps	12 final numbers
17	1,140	9 fixed pts	10 cycles	3 nodes	2.83 avg steps	7 max steps	4.09 avg steps	8 max steps	12 final numbers
18	1,330	16 fixed pts	16 cycles	1 node	3.02 avg steps	6 max steps	4.02 avg steps	7 max steps	16 final numbers
19	1,540	12 fixed pts	12 cycles	1 node	2.94 avg steps	6 max steps	3.94 avg steps	7 max steps	12 final numbers
20	1,771	18 fixed pts	19 cycles	3 nodes	2.84 avg steps	7 max steps	4.05 avg steps	8 max steps	21 final numbers
21	2,024	16 fixed pts	16 cycles	1 node	2.92 avg steps	7 max steps	3.92 avg steps	8 max steps	16 final numbers
22	2,300	22 fixed pts	22 cycles	1 node	2.91 avg steps	7 max steps	3.91 avg steps	8 max steps	22 final numbers
23	2,600	18 fixed pts	19 cycles	3 nodes	2.79 avg steps	7 max steps	3.93 avg steps	8 max steps	21 final numbers
24	2,925	27 fixed pts	27 cycles	1 node	2.90 avg steps	7 max steps	3.90 avg steps	8 max steps	27 final numbers
25	3,276	22 fixed pts	22 cycles	1 node	2.86 avg steps	7 max steps	3.86 avg steps	8 max steps	22 final numbers
26	3,654	30 fixed pts	31 cycles	3 nodes	2.80 avg steps	7 max steps	3.93 avg steps	8 max steps	33 final numbers
27	4,060	27 fixed pts	27 cycles	1 node	2.83 avg steps	7 max steps	3.83 avg steps	8 max steps	27 final numbers
28	4,495	35 fixed pts	35 cycles	1 node	2.85 avg steps	7 max steps	3.85 avg steps	8 max steps	35 final numbers
29	4,960	30 fixed pts	31 cycles	3 nodes	2.77 avg steps	7 max steps	3.86 avg steps	8 max steps	33 final numbers
30	5,456	41 fixed pts	41 cycles	1 node	2.85 avg steps	7 max steps	3.85 avg steps	8 max steps	41 final numbers
31	5,984	35 fixed pts	35 cycles	1 node	2.80 avg steps	7 max steps	3.80 avg steps	8 max steps	35 final numbers
32	6,545	45 fixed pts	46 cycles	3 nodes	2.77 avg steps	7 max steps	3.85 avg steps	8 max steps	48 final numbers
33	7,140	41 fixed pts	41 cycles	1 node	2.79 avg steps	7 max steps	3.79 avg steps	8 max steps	41 final numbers
34	7,770	51 fixed pts	51 cycles	1 node	2.81 avg steps	7 max steps	3.81 avg steps	8 max steps	51 final numbers
35	8,436	45 fixed pts	46 cycles	3 nodes	2.75 avg steps	7 max steps	3.81 avg steps	8 max steps	48 final numbers
36	9,139	58 fixed pts	58 cycles	1 node	2.80 avg steps	7 max steps	3.80 avg steps	8 max steps	58 final numbers
37	9,880	51 fixed pts	51 cycles	1 node	2.76 avg steps	7 max steps	3.76 avg steps	8 max steps	51 final numbers
38	10,660	63 fixed pts	64 cycles	3 nodes	2.75 avg steps	7 max steps	3.81 avg steps	10 max steps	66 final numbers
39	11,480	58 fixed pts	58 cycles	1 node	2.76 avg steps	8 max steps	3.76 avg steps	9 max steps	58 final numbers
40	12,341	70 fixed pts	70 cycles	1 node	2.78 avg steps	8 max steps	3.78 avg steps	9 max steps	70 final numbers
41	13,244	63 fixed pts	64 cycles	3 nodes	2.73 avg steps	8 max steps	3.77 avg steps	9 max steps	66 final numbers
42	14,190	78 fixed pts	78 cycles	1 node	2.77 avg steps	8 max steps	3.77 avg steps	9 max steps	78 final numbers
43	15,180	70 fixed pts	70 cycles	1 node	2.74 avg steps	8 max steps	3.74 avg steps	9 max steps	70 final numbers
44	16,215	84 fixed pts	85 cycles	3 nodes	2.73 avg steps	8 max steps	3.78 avg steps	9 max steps	87 final numbers
45	17,296	78 fixed pts	78 cycles	1 node	2.74 avg steps	8 max steps	3.74 avg steps	9 max steps	78 final numbers
46	18,424	92 fixed pts	92 cycles	1 node	2.75 avg steps	8 max steps	3.75 avg steps	9 max steps	92 final numbers
47	19,600	84 fixed pts	85 cycles	3 nodes	2.71 avg steps	8 max steps	3.74 avg steps	9 max steps	87 final numbers
48	20,825	101 fixed pts	101 cycles	1 node	2.75 avg steps	8 max steps	3.75 avg steps	9 max steps	101 final numbers
49	22,100	92 fixed pts	92 cycles	1 node	2.72 avg steps	8 max steps	3.72 avg steps	9 max steps	92 final numbers
50	23,426	108 fixed pts	109 cycles	3 nodes	2.72 avg steps	8 max steps	3.76 avg steps	9 max steps	111 final numbers
51	24,804	101 fixed pts	101 cycles	1 node	2.72 avg steps	8 max steps	3.72 avg steps	9 max steps	101 final numbers
52	26,235	117 fixed pts	117 cycles	1 node	2.73 avg steps	8 max steps	3.73 avg steps	9 max steps	117 final numbers
53	27,720	108 fixed pts	109 cycles	3 nodes	2.70 avg steps	8 max steps	3.72 avg steps	9 max steps	111 final numbers
54	29,260	127 fixed pts	127 cycles	1 node	2.73 avg steps	8 max steps	3.73 avg steps	9 max steps	127 final numbers
55	30,856	117 fixed pts	117 cycles	1 node	2.71 avg steps	8 max steps	3.71 avg steps	9 max steps	117 final numbers
56	32,509	135 fixed pts	136 cycles	3 nodes	2.71 avg steps	8 max steps	3.74 avg steps	9 max steps	138 final numbers
57	34,220	127 fixed pts	127 cycles	1 node	2.71 avg steps	8 max steps	3.71 avg steps	9 max steps	127 final numbers
58	35,990	145 fixed pts	145 cycles	1 node	2.72 avg steps	8 max steps	3.72 avg steps	9 max steps	145 final numbers
59	37,820	135 fixed pts	136 cycles	3 nodes	2.69 avg steps	8 max steps	3.71 avg steps	9 max steps	138 final numbers
60	39,711	156 fixed pts	156 cycles	1 node	2.72 avg steps	8 max steps	3.72 avg steps	9 max steps	156 final numbers
61	41,664	145 fixed pts	145 cycles	1 node	2.70 avg steps	8 max steps	3.70 avg steps	9 max steps	145 final numbers
62	43,680	165 fixed pts	166 cycles	3 nodes	2.70 avg steps	8 max steps	3.72 avg steps	9 max steps	168 final numbers
63	45,760	156 fixed pts	156 cycles	1 node	2.70 avg steps	8 max steps	3.70 avg steps	9 max steps	156 final numbers
64	47,905	176 fixed pts	176 cycles	1 node	2.71 avg steps	8 max steps	3.71 avg steps	9 max steps	176 final numbers
65	50,116	165 fixed pts	166 cycles	3 nodes	2.68 avg steps	8 max steps	3.70 avg steps	9 max steps	168 final numbers
66	52,394	188 fixed pts	188 cycles	1 node	2.71 avg steps	8 max steps	3.71 avg steps	9 max steps	188 final numbers
67	54,740	176 fixed pts	176 cycles	1 node	2.69 avg steps	8 max steps	3.69 avg steps	9 max steps	176 final numbers
68	57,155	198 fixed pts	199 cycles	3 nodes	2.69 avg steps	8 max steps	3.71 avg steps	9 max steps	201 final numbers
69	59,640	188 fixed pts	188 cycles	1 node	2.69 avg steps	8 max steps	3.69 avg steps	9 max steps	188 final numbers
70	62,196	210 fixed pts	210 cycles	1 node	2.70 avg steps	8 max steps	3.70 avg steps	9 max steps	210 final numbers
71	64,824	198 fixed pts	199 cycles	3 nodes	2.68 avg steps	8 max steps	3.69 avg steps	9 max steps	201 final numbers
72	67,525	223 fixed pts	223 cycles	1 node	2.69 avg steps	8 max steps	3.69 avg steps	9 max steps	223 final numbers
73	70,300	210 fixed pts	210 cycles	1 node	2.68 avg steps	8 max steps	3.68 avg steps	9 max steps	210 final numbers
74	73,150	234 fixed pts	235 cycles	3 nodes	2.68 avg steps	8 max steps	3.70 avg steps	11 max steps	237 final numbers
75	76,076	223 fixed pts	223 cycles	1 node	2.68 avg steps	9 max steps	3.68 avg steps	10 max steps	223 final numbers
76	79,079	247 fixed pts	247 cycles	1 node	2.69 avg steps	9 max steps	3.69 avg steps	10 max steps	247 final numbers
77	82,160	234 fixed pts	235 cycles	3 nodes	2.67 avg steps	9 max steps	3.68 avg steps	10 max steps	237 final numbers
78	85,320	261 fixed pts	261 cycles	1 node	2.69 avg steps	9 max steps	3.69 avg steps	10 max steps	261 final numbers
79	88,560	247 fixed pts	247 cycles	1 node	2.67 avg steps	9 max steps	3.67 avg steps	10 max steps	247 final numbers
80	91,881	273 fixed pts	274 cycles	3 nodes	2.68 avg steps	9 max steps	3.69 avg steps	10 max steps	276 final numbers
81	95,284	261 fixed pts	261 cycles	1 node	2.67 avg steps	9 max steps	3.67 avg steps	10 max steps	261 final numbers
82	98,770	287 fixed pts	287 cycles	1 node	2.68 avg steps	9 max steps	3.68 avg steps	10 max steps	287 final numbers
83	102,340	273 fixed pts	274 cycles	3 nodes	2.66 avg steps	9 max steps	3.67 avg steps	10 max steps	276 final numbers
84	105,995	302 fixed pts	302 cycles	1 node	2.68 avg steps	9 max steps	3.68 avg steps	10 max steps	302 final numbers
85	109,736	287 fixed pts	287 cycles	1 node	2.67 avg steps	9 max steps	3.67 avg steps	10 max steps	287 final numbers
86	113,564	315 fixed pts	316 cycles	3 nodes	2.67 avg steps	9 max steps	3.68 avg steps	10 max steps	318 final numbers
87	117,480	302 fixed pts	302 cycles	1 node	2.67 avg steps	9 max steps	3.67 avg steps	10 max steps	302 final numbers
88	121,485	330 fixed pts	330 cycles	1 node	2.68 avg steps	9 max steps	3.68 avg steps	10 max steps	330 final numbers
89	125,580	315 fixed pts	316 cycles	3 nodes	2.66 avg steps	9 max steps	3.67 avg steps	10 max steps	318 final numbers
90	129,766	346 fixed pts	346 cycles	1 node	2.68 avg steps	9 max steps	3.68 avg steps	10 max steps	346 final numbers
91	134,044	330 fixed pts	330 cycles	1 node	2.66 avg steps	9 max steps	3.66 avg steps	10 max steps	330 final numbers
92	138,415	360 fixed pts	361 cycles	3 nodes	2.67 avg steps	9 max steps	3.68 avg steps	10 max steps	363 final numbers
93	142,880	346 fixed pts	346 cycles	1 node	2.66 avg steps	9 max steps	3.66 avg steps	10 max steps	346 final numbers
94	147,440	376 fixed pts	376 cycles	1 node	2.67 avg steps	9 max steps	3.67 avg steps	10 max steps	376 final numbers
95	152,096	360 fixed pts	361 cycles	3 nodes	2.66 avg steps	9 max steps	3.66 avg steps	10 max steps	363 final numbers
96	156,849	393 fixed pts	393 cycles	1 node	2.67 avg steps	9 max steps	3.67 avg steps	10 max steps	393 final numbers
97	161,700	376 fixed pts	376 cycles	1 node	2.66 avg steps	9 max steps	3.66 avg steps	10 max steps	376 final numbers
98	166,650	408 fixed pts	409 cycles	3 nodes	2.66 avg steps	9 max steps	3.67 avg steps	10 max steps	411 final numbers
99	171,700	393 fixed pts	393 cycles	1 node	2.66 avg steps	9 max steps	3.66 avg steps	10 max steps	393 final numbers
100	176,851	425 fixed pts	425 cycles	1 node	2.67 avg steps	9 max steps	3.67 avg steps	10 max steps	425 final numbers