Base 3: Iteration Frequencies: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets]
[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] — [2] [Base 3] [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]
[Full Cycle]
Maximum Iteration Sequences
[Cycle Start]
[Full Cycle]
Cycles Sequences
[Maximum Length Cycle Count]
[All Cycle Counts]

Radix Character Encoding
0	1	2

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	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
Average Steps Cycle Start	0.67 step avg	1.67 step avg	0.80 step avg	1.40 step avg	2.14 step avg	1.64 step avg	1.86 step avg	2.80 step avg	1.69 step avg	2.09 step avg	1.58 step avg	2.87 step avg	1.50 step avg	3.17 step avg	1.43 step avg	2.58 step avg	1.39 step avg	2.37 step avg	1.35 step avg	2.83 step avg	1.32 step avg	2.96 step avg	1.29 step avg	2.61 step avg	1.27 step avg	3.17 step avg	1.25 step avg	2.59 step avg	1.23 step avg	2.69 step avg	1.22 step avg	2.46 step avg	1.21 step avg	2.50 step avg	1.19 step avg	2.72 step avg	1.18 step avg	2.78 step avg	1.17 step avg	2.59 step avg	1.17 step avg	2.88 step avg	1.16 step avg	2.56 step avg	1.15 step avg	2.62 step avg	1.15 step avg	2.47 step avg	1.14 step avg	2.99 step avg	1.13 step avg	2.54 step avg	1.13 step avg	2.58 step avg	1.12 step avg	2.46 step avg	1.12 step avg	2.66 step avg	1.12 step avg	2.46 step avg	1.11 step avg	2.49 step avg	1.11 step avg	2.40 step avg	1.11 step avg	2.52 step avg	1.10 step avg	2.60 step avg	1.10 step avg	2.63 step avg	1.10 step avg	2.53 step avg	1.09 step avg	2.67 step avg	1.09 step avg	2.52 step avg	1.09 step avg	2.54 step avg	1.09 step avg	2.46 step avg	1.09 step avg	2.73 step avg	1.08 step avg	2.50 step avg	1.08 step avg	2.52 step avg	1.08 step avg	2.45 step avg	1.08 step avg	2.56 step avg	1.08 step avg	2.44 step avg	1.07 step avg	2.47 step avg	1.07 step avg	2.40 step avg	1.07 step avg	2.78 step avg	1.07 step avg	2.48 step avg
Step Frequency Cycle Start	0s: 1s: 1× 2×	0s: 1s: 2s: 3s: 1× 2× 1× 2×	0s: 1s: 2× 8×	0s: 1s: 2s: 1× 7× 7×	0s: 1s: 2s: 3s: 4s: 1× 6× 7× 3× 4×	0s: 1s: 2s: 3s: 1× 11× 13× 3×	0s: 1s: 2s: 3s: 4s: 1× 14× 14× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 1× 6× 15× 5× 15× 3×	0s: 1s: 2s: 3s: 4s: 1× 26× 21× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 1× 19× 32× 4× 7× 3×	0s: 1s: 2s: 3s: 4s: 1× 42× 28× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 1× 14× 34× 7× 19× 14× 2×	0s: 1s: 2s: 3s: 4s: 1× 62× 35× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 1× 18× 30× 23× 16× 22× 10×	0s: 1s: 2s: 3s: 4s: 1× 86× 42× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 1× 30× 61× 20× 25× 14× 2×	0s: 1s: 2s: 3s: 4s: 1× 114× 49× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 1× 47× 74× 35× 17× 14× 2×	0s: 1s: 2s: 3s: 4s: 1× 146× 56× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 46× 88× 22× 29× 22× 21× 2×	0s: 1s: 2s: 3s: 4s: 1× 182× 63× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 54× 80× 54× 26× 30× 29× 2×	0s: 1s: 2s: 3s: 4s: 1× 222× 70× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 74× 127× 43× 35× 22× 21× 2×	0s: 1s: 2s: 3s: 4s: 1× 266× 77× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 78× 99× 56× 62× 27× 29× 10× 16×	0s: 1s: 2s: 3s: 4s: 1× 314× 84× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 102× 166× 53× 58× 32× 21× 2×	0s: 1s: 2s: 3s: 4s: 1× 366× 91× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 114× 154× 101× 55× 40× 29× 2×	0s: 1s: 2s: 3s: 4s: 1× 422× 98× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 142× 217× 82× 64× 32× 21× 2×	0s: 1s: 2s: 3s: 4s: 1× 482× 105× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 163× 210× 113× 88× 32× 21× 2×	0s: 1s: 2s: 3s: 4s: 1× 546× 112× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 174× 260× 84× 68× 40× 37× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 614× 119× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 190× 244× 148× 65× 48× 45× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 686× 126× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 226× 323× 121× 74× 40× 37× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 762× 133× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 234× 275× 150× 133× 45× 45× 45× 18×	0s: 1s: 2s: 3s: 4s: 1× 842× 140× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 274× 382× 139× 113× 50× 37× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 926× 147× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 294× 362× 219× 110× 58× 45× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 1,014× 154× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 338× 457× 184× 119× 50× 37× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 1,106× 161× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 1× 342× 381× 197× 143× 117× 42× 45× 10× 16× 32×	0s: 1s: 2s: 3s: 4s: 1× 1,202× 168× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 390× 520× 194× 139× 93× 55× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 1,302× 175× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 414× 496× 290× 136× 101× 63× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 1,406× 182× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 466× 607× 247× 145× 93× 55× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 1,514× 189× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 478× 539× 292× 236× 98× 63× 45× 18×	0s: 1s: 2s: 3s: 4s: 1× 1,626× 196× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 534× 686× 273× 200× 103× 55× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 1,742× 203× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 562× 658× 385× 197× 111× 63× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 1,862× 210× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 622× 785× 334× 206× 103× 55× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 1,986× 217× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 647× 726× 381× 262× 167× 55× 37× 2×	0s: 1s: 2s: 3s: 4s: 1× 2,114× 224× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 686× 860× 336× 210× 111× 71× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 2,246× 231× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 718× 828× 464× 207× 119× 79× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 2,382× 238× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 786× 971× 405× 216× 111× 71× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 2,522× 245× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 802× 883× 466× 339× 116× 79× 77× 85× 2×	0s: 1s: 2s: 3s: 4s: 1× 2,666× 252× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 874× 1,070× 439× 287× 121× 71× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 2,814× 259× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 910× 1,034× 583× 284× 129× 79× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 2,966× 266× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 986× 1,193× 516× 293× 121× 71× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 3,122× 273× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 1× 994× 1,065× 545× 349× 252× 76× 77× 77× 18× 32×	0s: 1s: 2s: 3s: 4s: 1× 3,282× 280× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 1,074× 1,292× 534× 329× 196× 89× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 3,446× 287× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 1,114× 1,252× 694× 326× 204× 97× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 3,614× 294× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 1,198× 1,427× 619× 335× 196× 89× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 3,786× 301× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 1,218× 1,319× 696× 490× 201× 97× 77× 85× 2×	0s: 1s: 2s: 3s: 4s: 1× 3,962× 308× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 1,306× 1,546× 661× 422× 206× 89× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 4,142× 315× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 1,350× 1,502× 837× 419× 214× 97× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 4,326× 322× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 1,442× 1,693× 754× 428× 206× 89× 69× 69× 2×	0s: 1s: 2s: 3s: 4s: 1× 4,514× 329× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 1× 1,446× 1,521× 767× 452× 270× 220× 74× 77× 10× 16× 32× 64×	0s: 1s: 2s: 3s: 4s: 1× 4,706× 336× 3× 4×	0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 1,542× 1,804× 764× 448× 246× 172× 103× 69× 2×