Base 5: Cycles Lengths: Odd Digit Sets

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] — [2] [3] [4] [Base 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]
[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

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	# Full Cycles (excluding zero)	Nodes
Digits	# Full Cycles (excluding zero)	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
1	0 cycles	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
3	1 cycle	-	30×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
5	1 cycle	-	-	-	121×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
7	1 cycle	-	-	-	325×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
9	1 cycle	710×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
11	2 cycles	28×	-	1,332×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
13	3 cycles	28×	-	124×	-	2,223×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
15	6 cycles	28×	395×	124×	694×	253×	2,377×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
17	9 cycles	28×	821×	124×	4,162×	253×	592×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
19	14 cycles	28×	304×	1,019×	6,654×	253×	592×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
21	16 cycles	28×	304×	649×	3,144×	253×	592×	-	-	7,675×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
23	23 cycles	520×	634×	1,716×	3,144×	253×	8,899×	-	-	2,379×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
25	26 cycles	206×	392×	906×	3,144×	253×	3,295×	-	-	2,379×	-	13,171×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
27	30 cycles	206×	392×	906×	3,144×	253×	3,295×	-	-	2,379×	16,515×	4,370×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
29	36 cycles	206×	392×	2,324×	3,144×	253×	3,295×	-	-	21,073×	5,858×	4,370×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
31	40 cycles	206×	392×	1,461×	3,144×	253×	3,295×	-	-	9,248×	5,858×	4,370×	-	-	24,128×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
33	54 cycles	206×	392×	1,461×	4,224×	28,244×	3,295×	-	-	9,248×	5,858×	4,370×	-	-	8,742×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
35	68 cycles	206×	392×	1,461×	3,144×	45,530×	3,295×	-	-	9,248×	5,858×	4,370×	-	-	8,742×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
37	77 cycles	775×	392×	1,461×	3,144×	24,677×	9,673×	-	-	9,248×	5,858×	4,370×	32,925×	-	8,742×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
39	83 cycles	386×	392×	1,461×	3,144×	24,677×	9,599×	-	-	9,248×	5,858×	4,370×	12,981×	-	8,742×	-	-	-	42,547×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
41	95 cycles	386×	1,282×	1,461×	4,368×	24,677×	18,470×	-	-	9,248×	5,858×	4,370×	53,373×	-	8,742×	-	-	-	16,755×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
43	107 cycles	386×	781×	1,461×	3,656×	24,677×	10,466×	-	-	9,248×	67,193×	4,370×	30,625×	-	8,742×	-	-	-	16,755×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
45	126 cycles	386×	781×	1,461×	3,656×	24,677×	10,466×	70,243×	-	9,248×	30,461×	4,370×	30,625×	-	8,742×	-	-	-	16,755×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
47	144 cycles	386×	2,406×	3,415×	11,378×	24,677×	16,163×	28,884×	-	9,248×	30,461×	4,370×	93,010×	-	8,742×	-	-	-	16,755×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
49	150 cycles	386×	1,495×	2,233×	5,704×	24,677×	12,922×	28,884×	-	9,248×	30,461×	4,370×	57,620×	-	8,742×	-	-	-	16,755×	-	-	-	-	89,323×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
51	160 cycles	1,062×	1,495×	2,233×	5,704×	24,677×	12,922×	32,017×	-	9,248×	30,461×	4,370×	57,620×	-	8,742×	-	-	-	16,755×	-	-	96,826×	-	36,918×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
53	188 cycles	630×	1,495×	2,233×	24,887×	24,677×	12,922×	30,333×	93,053×	9,248×	30,461×	4,370×	57,620×	-	8,742×	-	-	-	16,755×	-	-	40,661×	-	36,918×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
55	196 cycles	630×	1,495×	2,233×	13,856×	24,677×	12,922×	30,333×	39,564×	9,248×	30,461×	4,370×	57,620×	-	8,742×	-	-	-	16,755×	-	-	40,661×	-	36,918×	-	-	124,636×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
57	209 cycles	630×	1,495×	2,233×	13,856×	27,608×	12,922×	30,333×	39,564×	9,248×	43,230×	4,370×	57,620×	-	8,742×	-	-	-	16,755×	-	123,027×	40,661×	-	36,918×	-	-	52,638×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
59	238 cycles	630×	1,495×	6,726×	13,856×	25,945×	12,922×	30,333×	39,564×	157,790×	36,060×	4,370×	57,620×	-	8,742×	-	-	-	16,755×	-	52,635×	40,661×	-	36,918×	-	-	52,638×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
61	247 cycles	630×	1,495×	4,210×	13,856×	25,945×	12,922×	30,333×	39,564×	73,418×	36,060×	4,370×	57,620×	-	8,742×	-	-	-	16,755×	-	52,635×	40,661×	-	36,918×	-	-	52,638×	-	-	168,263×	-	-	-	-	-	-	-	-	-	-	-	-
63	257 cycles	630×	1,495×	4,210×	13,856×	25,945×	12,922×	30,333×	39,564×	73,418×	41,326×	4,370×	57,620×	-	8,742×	-	-	-	16,755×	-	52,635×	40,661×	-	36,918×	-	-	52,638×	-	-	72,416×	180,021×	-	-	-	-	-	-	-	-	-	-	-
65	313 cycles	1,490×	2,158×	24,280×	13,856×	25,945×	194,016×	30,333×	39,564×	73,418×	38,649×	4,370×	57,620×	-	8,742×	-	-	-	16,755×	-	52,635×	40,661×	-	36,918×	-	-	52,638×	-	-	72,416×	78,032×	-	-	-	-	-	-	-	-	-	-	-
67	367 cycles	938×	3,217×	11,768×	13,856×	25,945×	313,155×	30,333×	39,564×	73,418×	38,649×	4,370×	57,620×	-	8,742×	-	-	-	16,755×	-	52,635×	40,661×	-	36,918×	-	-	52,638×	-	-	72,416×	78,032×	-	-	-	-	-	-	-	-	-	-	-
69	378 cycles	938×	2,412×	11,768×	13,856×	25,945×	189,475×	30,333×	39,564×	73,418×	38,649×	12,939×	57,620×	-	8,742×	-	-	-	16,755×	-	52,635×	40,661×	-	36,918×	-	-	52,638×	-	-	72,416×	78,032×	-	-	232,711×	-	-	-	-	-	-	-	-
71	397 cycles	938×	2,412×	11,768×	13,856×	25,945×	189,475×	30,333×	39,564×	73,418×	38,649×	45,749×	57,620×	-	8,742×	-	-	-	16,755×	-	52,635×	40,661×	223,658×	36,918×	-	-	52,638×	-	-	72,416×	78,032×	-	-	103,263×	-	-	-	-	-	-	-	-
73	408 cycles	938×	2,412×	11,768×	13,856×	25,945×	189,475×	30,333×	39,564×	73,418×	38,649×	24,134×	57,620×	-	8,742×	-	-	-	16,755×	-	52,635×	40,661×	99,351×	36,918×	-	-	52,638×	-	-	72,416×	78,032×	-	-	103,263×	-	283,747×	-	-	-	-	-	-
75	456 cycles	938×	2,412×	23,443×	13,856×	25,945×	189,475×	30,333×	39,564×	369,378×	38,649×	24,134×	57,620×	-	8,742×	-	-	-	16,755×	-	52,635×	40,661×	99,351×	36,918×	-	-	52,638×	-	-	72,416×	78,032×	-	-	103,263×	-	125,338×	-	-	-	-	-	-
77	484 cycles	938×	4,774×	17,053×	21,087×	25,945×	189,475×	30,333×	39,564×	205,148×	85,997×	24,134×	57,620×	-	8,742×	-	-	-	16,755×	-	327,553×	40,661×	99,351×	36,918×	-	-	52,638×	-	-	72,416×	78,032×	-	-	103,263×	-	125,338×	-	-	-	-	-	-
79	502 cycles	1,934×	3,500×	17,053×	17,016×	29,797×	189,475×	30,333×	39,564×	205,148×	58,501×	24,134×	57,620×	-	8,742×	22,357×	-	-	16,755×	-	177,023×	40,661×	99,351×	36,918×	-	-	52,638×	-	-	72,416×	408,078×	-	-	103,263×	-	125,338×	-	-	-	-	-	-
81	515 cycles	1,310×	3,500×	17,053×	17,016×	27,693×	189,475×	30,333×	39,564×	205,148×	58,501×	24,134×	57,620×	14,319×	8,742×	10,663×	-	-	16,755×	-	177,023×	40,661×	99,351×	36,918×	-	-	52,638×	-	-	72,416×	224,578×	-	-	103,263×	-	125,338×	-	-	-	370,768×	-	-
83	538 cycles	1,310×	3,500×	20,225×	17,016×	27,693×	189,475×	30,333×	39,564×	244,369×	58,501×	24,134×	57,620×	4,329×	8,742×	10,663×	-	-	16,755×	-	177,023×	40,661×	99,351×	36,918×	-	-	52,638×	370,794×	-	72,416×	224,578×	-	-	103,263×	-	125,338×	-	-	-	168,681×	-	-
85	551 cycles	1,310×	3,500×	18,401×	17,016×	27,693×	189,475×	30,333×	39,564×	221,124×	58,501×	24,134×	57,620×	4,329×	8,742×	10,663×	-	-	16,755×	-	177,023×	40,661×	99,351×	36,918×	-	-	52,638×	169,071×	-	72,416×	224,578×	-	-	103,263×	-	125,338×	-	-	-	168,681×	-	442,523×
87	627 cycles	1,310×	3,500×	18,401×	57,594×	27,693×	189,475×	30,333×	473,413×	221,124×	58,501×	24,134×	57,620×	4,329×	8,742×	10,663×	-	-	16,755×	-	177,023×	40,661×	99,351×	36,918×	-	-	52,638×	169,071×	-	72,416×	224,578×	-	-	103,263×	-	125,338×	-	-	-	168,681×	-	199,140×
89	651 cycles	1,310×	3,500×	18,401×	35,790×	27,693×	189,475×	30,333×	235,475×	221,124×	58,501×	24,134×	57,620×	4,329×	85,019×	10,663×	-	-	16,755×	-	177,023×	40,661×	99,351×	36,918×	-	-	52,638×	169,071×	430,530×	72,416×	224,578×	-	-	103,263×	-	125,338×	-	-	-	168,681×	-	199,140×
91	707 cycles	1,310×	3,500×	18,401×	35,790×	27,693×	189,475×	30,333×	235,475×	221,124×	58,501×	564,557×	57,620×	4,329×	41,308×	10,663×	-	-	16,755×	-	177,023×	40,661×	99,351×	36,918×	-	-	52,638×	169,071×	197,628×	72,416×	224,578×	-	-	103,263×	-	125,338×	-	-	-	168,681×	-	199,140×
93	768 cycles	2,490×	5,308×	18,401×	46,481×	27,693×	228,971×	30,333×	235,475×	221,124×	58,501×	269,089×	581,208×	4,329×	41,308×	10,663×	-	-	16,755×	-	177,023×	40,661×	99,351×	36,918×	-	-	52,638×	169,071×	197,628×	72,416×	224,578×	-	-	103,263×	-	125,338×	-	-	-	168,681×	-	199,140×
95	845 cycles	1,746×	4,316×	18,401×	41,359×	115,180×	206,765×	30,333×	235,475×	221,124×	584,501×	269,089×	296,321×	4,329×	41,308×	10,663×	-	-	16,755×	-	177,023×	40,661×	99,351×	36,918×	-	-	52,638×	169,071×	197,628×	72,416×	224,578×	-	-	103,263×	-	125,338×	-	-	-	168,681×	-	199,140×
97	868 cycles	1,746×	4,316×	20,706×	41,359×	65,688×	206,765×	30,333×	235,475×	238,182×	300,803×	269,089×	296,321×	4,329×	41,308×	10,663×	-	-	51,699×	-	177,023×	40,661×	99,351×	36,918×	-	-	52,638×	169,071×	197,628×	72,416×	224,578×	-	-	103,263×	-	125,338×	597,432×	-	-	168,681×	-	199,140×
99	900 cycles	1,746×	4,316×	19,629×	41,359×	65,688×	206,765×	30,333×	251,139×	228,580×	300,803×	269,089×	296,321×	4,329×	41,308×	10,663×	-	-	31,381×	-	177,023×	40,661×	99,351×	36,918×	677,147×	-	52,638×	169,071×	197,628×	72,416×	224,578×	-	-	103,263×	-	125,338×	273,968×	-	-	168,681×	-	199,140×