Base 198: Cycles Sequences: Maximum Length Cycle Count

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]
[Full Cycle]
Maximum Iteration Sequences
[Cycle Start]
[Full Cycle]
Cycles Sequences
[Maximum Length Cycle Count] — [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] [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] [Base 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]
[All Cycle Counts]

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
m	n	o	p	q	r	s	t	u	v	w	x	y	z	Α	Β
Γ	Δ	Ε	Ζ	Η	Θ	Ι	Κ	Λ	Μ	Ν	Ξ	Ο	Π	Ρ	Σ
Τ	Υ	Φ	Χ	Ψ	Ω	α	β	γ	δ	ε	ζ	η	θ	ι	κ
λ	μ	ν	ξ	ο	π	ρ	ς	σ	τ	υ	φ	χ	ψ	ω	А
Б	В	Г	Д	Е	Ж	З	И	Й	К	Л	М	Н	О	П	Р
С	Т	У	Ф	Х	Ц	Ч	Ш	Щ	Ъ	Ы	Ь	Э	Ю	Я	а
б	в	г	д	е	ж	з	и	й	к	л	м	н	о	п	р
с	т	у	ф	х	ц	ч	ш	щ	ъ	ы	ь	э	ю	я	ァ
ア	ィ	イ	ゥ	ウ	ェ	エ	ォ	オ	カ	ガ	キ	ギ	ク	グ	ケ
ゲ	コ	ゴ	サ	ザ	シ	ジ	ス	ズ	セ	ゼ	ソ	ゾ	タ	ダ	チ

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)	Max Cycle Length	Longest Full Cycles (excluding zero) (bold = exactly one cycle [excluding zero])
1	0 cycles	-	-
2	1 cycle	99 nodes	⮎ 0シ → ザ1 → ゴ3 → グ7 → エF → чV → ЧΒ → ΙР → uЮ → ΨВ → Sъ → Эv → ΦД → Wц → ХΔ → ΕФ → ΓЦ → ΗТ → yЪ → ΟК → iк → χδ → Iゥ → сb → ЛΞ → kи → σθ → Aキ → アL → лh → ωβ → Mァ → йj → υζ → Eォ → щT → Ыx → ΡИ → eо → ЕΥ → Yф → СΘ → wЬ → ΤЖ → aт → НΜ → oд → λπ → 4コ → ギ9 → イJ → пd → ЗΣ → cр → ЙΠ → gм → БΩ → Qь → бr → εφ → Gェ → хX → УΖ → ΑШ → ΛО → qв → ητ → Cカ → эP → гp → ις → 8ク → ウH → уZ → ПΚ → sа → γψ → Kィ → нf → ГΧ → Uш → Щz → ΝМ → mж → ομ → 2サ → ゲ5 → ガB → яN → зl → ρκ → 6ケ → オD → ыR → Яt → αА → Oю → еn → νξ ⮌
3	1 cycle	(fixed) 1 node	⮎ νシξ ⮌
4	96 cycles	15 nodes	⮎ o1サе → ゴμξ4 → グ1サ8 → ゴェF4 → グцV8 → エЦΒG → чΘРW → ЧvЬΓ → ΦΘРЕ → wXфЭ → УΥДΗ → ΑXфЩ → УΜМΗ → ΑnдЩ → νΜМο ⮌
5	2 cycles	2 nodes	⮎ ξμシξξ → ξシシシν ⮌

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
m	n	o	p	q	r	s	t	u	v	w	x	y	z	Α	Β
Γ	Δ	Ε	Ζ	Η	Θ	Ι	Κ	Λ	Μ	Ν	Ξ	Ο	Π	Ρ	Σ
Τ	Υ	Φ	Χ	Ψ	Ω	α	β	γ	δ	ε	ζ	η	θ	ι	κ
λ	μ	ν	ξ	ο	π	ρ	ς	σ	τ	υ	φ	χ	ψ	ω	А
Б	В	Г	Д	Е	Ж	З	И	Й	К	Л	М	Н	О	П	Р
С	Т	У	Ф	Х	Ц	Ч	Ш	Щ	Ъ	Ы	Ь	Э	Ю	Я	а
б	в	г	д	е	ж	з	и	й	к	л	м	н	о	п	р
с	т	у	ф	х	ц	ч	ш	щ	ъ	ы	ь	э	ю	я	ァ
ア	ィ	イ	ゥ	ウ	ェ	エ	ォ	オ	カ	ガ	キ	ギ	ク	グ	ケ
ゲ	コ	ゴ	サ	ザ	シ	ジ	ス	ズ	セ	ゼ	ソ	ゾ	タ	ダ	チ

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
m	n	o	p	q	r	s	t	u	v	w	x	y	z	Α	Β
Γ	Δ	Ε	Ζ	Η	Θ	Ι	Κ	Λ	Μ	Ν	Ξ	Ο	Π	Ρ	Σ
Τ	Υ	Φ	Χ	Ψ	Ω	α	β	γ	δ	ε	ζ	η	θ	ι	κ
λ	μ	ν	ξ	ο	π	ρ	ς	σ	τ	υ	φ	χ	ψ	ω	А
Б	В	Г	Д	Е	Ж	З	И	Й	К	Л	М	Н	О	П	Р
С	Т	У	Ф	Х	Ц	Ч	Ш	Щ	Ъ	Ы	Ь	Э	Ю	Я	а
б	в	г	д	е	ж	з	и	й	к	л	м	н	о	п	р
с	т	у	ф	х	ц	ч	ш	щ	ъ	ы	ь	э	ю	я	ァ
ア	ィ	イ	ゥ	ウ	ェ	エ	ォ	オ	カ	ガ	キ	ギ	ク	グ	ケ
ゲ	コ	ゴ	サ	ザ	シ	ジ	ス	ズ	セ	ゼ	ソ	ゾ	タ	ダ	チ

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
m	n	o	p	q	r	s	t	u	v	w	x	y	z	Α	Β
Γ	Δ	Ε	Ζ	Η	Θ	Ι	Κ	Λ	Μ	Ν	Ξ	Ο	Π	Ρ	Σ
Τ	Υ	Φ	Χ	Ψ	Ω	α	β	γ	δ	ε	ζ	η	θ	ι	κ
λ	μ	ν	ξ	ο	π	ρ	ς	σ	τ	υ	φ	χ	ψ	ω	А
Б	В	Г	Д	Е	Ж	З	И	Й	К	Л	М	Н	О	П	Р
С	Т	У	Ф	Х	Ц	Ч	Ш	Щ	Ъ	Ы	Ь	Э	Ю	Я	а
б	в	г	д	е	ж	з	и	й	к	л	м	н	о	п	р
с	т	у	ф	х	ц	ч	ш	щ	ъ	ы	ь	э	ю	я	ァ
ア	ィ	イ	ゥ	ウ	ェ	エ	ォ	オ	カ	ガ	キ	ギ	ク	グ	ケ
ゲ	コ	ゴ	サ	ザ	シ	ジ	ス	ズ	セ	ゼ	ソ	ゾ	タ	ダ	チ