Base 27: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV

Color Key
OrangeFixed Pointnumber that becomes itself after one iteration
GreenFinal Numbersall numbers eventually reached, from all cycles
PurpleCycle Startiterations include entry into cycle, assuming it repeats
RedFull Cycleiterations include entire cycle, proving it repeats
BlueStart Numberssubset (optimization) of all numbers; minimal for full coverage
GrayNo Resultsany calculation that has no results

Digits # Full Cycles
(excluding zero)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
21 cycle 3 nodes⮎ 3N → J7 → BF ⮌
31 cycle 2 nodes⮎ CQE → DQD ⮌
410 cycles9 nodes⮎ 50PM → PG92 → N6J4 → JCD8 → B0PG → P4L2 → NG94 → J6J8 → DAFE ⮌
51 cycle (fixed) 1 node ⮎ I8QH9 ⮌
64 cycles58 nodes⮎ 740PMK → PICD82 → NA0PG4 → PJ5K72 → NFBEB4 → J42NM8 → LIAF86 → FA4LGC → H62NKA → LE6JC6 → FD1ODC → N2QQN4 → OLQQ43 → NM2N44 → LJH876 → FC8HEC → 931ONI → NK8H64 → JE8HC8 → B91OHG → N84LI4 → JH9G98 → B86JIG → DA4LGE → H60PKA → PE6JC2 → ND1OD4 → NIQQ74 → MJ4L75 → IGBEA9 → 962NKI → LE8HC6 → F91OHC → N82NI4 → LJ9G76 → FC6JEC → D31ONE → NK0P64 → PJDC72 → NC0PE4 → PJ1O72 → OMBE43 → LI2N86 → LF9GB6 → F73MJC → JC2NE8 → LB1OF6 → NF3MB4 → KI3M87 → JD9GD8 → B6QQJG → KF2NB7 → LD3MD6 → JEQQB8 → IF4LB9 → H93MHA → J86JI8 → DB9GFE ⮌
71 cycle 8 nodes⮎ KD3QMD7 → NF6QJB4 → MH7QI95 → LF8QHB6 → KD5QKD7 → LD6QJD6 → KF5QKB7 → LD8QHD6 ⮌
87 cycles25 nodes⮎ B431ONMG → NKI4L864 → JHE9GC98 → B871OJIG → NCA4LGE4 → JH61OK98 → NEB7IFC4 → JB41OMF8 → NIB3MF84 → KIA3MG87 → JDA5KGD8 → FB5QQKFC → LF7QQIB6 → KJA2NG77 → LDC5KED6 → GE1QQOCB → PFC1OEB2 → OM41OM43 → NLIH8854 → JGA8HGA8 → B965KKHG → FE84LICC → HA31ONGA → NK75KJ64 → JFEBECB8 ⮌
94 cycles8 nodes⮎ LGA4QLGA6 → MFB5QKFB5 → LH93QMH96 → NGC7QIEA4 → MG83QMIA5 → NHE7QIC94 → MG94QLHA5 → MHC6QJE95 ⮌
102 cycles6 nodes⮎ NJC21OOE74 → NMJC1OE744 → NJIC1OE874 → NJCA1OGE74 → NJC61OKE74 → NJEC1OEC74 ⮌
113 cycles15 nodes⮎ LHB62QNKF96 → OHFB5QKFB93 → NJB63QMKF74 → NJGD7QIDA74 → MGC82QNIEA5 → OIE83QMIC83 → NLEA5QKGC54 → MIGA3QMGA85 → NHE85QKIC94 → MIC94QLHE85 → MHD94QLHD95 → MHC83QMIE95 → NHE94QLHC94 → MJC84QLIE75 → MHEB5QKFC95 ⮌
126 cycles28 nodes⮎ BA7663MKKJGG → JEEC64LKECC8 → HEB221OOOFCA → NMM741OMJ444 → NJIIIBE88874 → JCAAA2NGGGE8 → LB6661OKKKF6 → NFEEE3MCCCB4 → KI4221OOOM87 → NMMID9GD8444 → JIIA6QQJG888 → KIBB81OIFF87 → NDAA43MMGGD4 → KII65QQKK887 → LKDCBQQEED66 → KKA810PPIG67 → POEDA5KGDC22 → NMF61QQOKB44 → PMKHB4LF9642 → NIHE83MIC984 → KIAA81OIGG87 → NDAA65KKGGD4 → JFE65QQKKCB8 → LKC970PJHE66 → PFEC81OIECB2 → OMA421OOMG43 → NMLII5K88544 → JIGFA9GGBA88 ⮌
135 cycles41 nodes⮎ MGC962QNKHEA5 → OIGB73QMJFA83 → NLFB84QLIFB54 → MJGD73QMJDA75 → NHFC92QNHEB94 → OJE862QNKIC73 → OLHDB5QKFD953 → NJGB61QOKFA74 → PKHD94QLHD962 → OLFB83QMIFB53 → NLHD73QMJD954 → NJHEA3QMGC974 → NJFA73QMJGB74 → NJFC94QLHEB74 → MJEA62QNKGC75 → OIGD93QMHDA83 → NLE972QNJHC54 → OJIEA4QLGC873 → NKEB83QMIFC64 → NJGC72QNJEA74 → OJGC93QMHEA73 → NLFA73QMJGB54 → NJHE94QLHC974 → MJEA84QLIGC75 → MHEB83QMIFC95 → NHE962QNKHC94 → OJHB84QLIF973 → NKEB95QKHFC64 → MIEB62QNKFC85 → OIGC72QNJEA83 → OLGB83QMIFA53 → NLHD84QLID954 → MJGD93QMHDA75 → NHFA72QNJGB94 → OJGA74QLJGA73 → NKEC95QKHEC64 → MIEB51QOLFC85 → PJHD72QNJD972 → ONGCA3QMGEA33 → NLKC63QMKE654 → NJHFE7QICB974 ⮌