Base 45: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl

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 11 nodes1h → f3 → b7 → TF → DV → HR → 9Z → PJ → 5d → XB → LN
31 cycle 2 nodesLiN → MiM
427 cycles12 nodesB0hY → hML2 → f0h4 → ha72 → fSF4 → bCV8 → TIPG → D6bW → VIPE → H6bS → VAXE → NGRM
51 cycle (fixed) 1 node UEiTF
67 cycles44 nodesEC5cWV → XKGROC → LB3eXO → bM2fM8 → dSiiF6 → cTAXF7 → VNDULE → IG1gSR → fC8ZW4 → bRJOH8 → TA4dYG → ZOCVKA → PJ3ePK → b64dc8 → ZWSFCA → PKCVOK → J53edQ → bY6bA8 → VTNKFE → HE2fUS → dGAXS6 → XNBWLC → MK1gON → f40he4 → hbZ872 → fUQHE4 → bG8ZS8 → TRBWHG → LD9YVO → PI2fQK → d84da6 → ZXRGBA → PMAXMK → N4iidM → eMFSM5 → ZCiiVA → YW3eCB → bNJOL8 → T51gdG → fYCVA4 → bOIPK8 → T73ebG → bUCVE8 → TJFSPG
73 cycles4 nodesWL9iYND → ZLAiXNA → YPBiWJB → XNCiVLC
87 cycles46 nodes6441geed → faaWB884 → bSSKNGG8 → TCC2fWWG → dKKCVOO6 → XJ43eePC → baL5cN88 → XTS1gGFC → fLEBWUN4 → bLG1gSN8 → fTC1gWF4 → fbKDUO74 → bUH3eRE8 → bTG9YSF8 → TPEBWUJG → LGD5cVSO → XIC2fWQC → dLK7aON6 → XT41geFC → faLDUN84 → bSH1gRG8 → fTC9YWF4 → bPKDUOJ8 → TH63ecRG → bWD9YVC8 → TPKHQOJG → D963ecZW → bWQIPIC8 → TK86baOG → VSD3eVGE → bIHBWRQ8 → TLA7aYNG → TOD1gVKG → fID3eVQ4 → caI7aQ87 → VTS7aGFE → THEBWURG → LGD9YVSO → PIC2fWQK → dK84daO6 → ZXS3eGBA → bPMBWMJ8 → TL5iicNG → dSH5cRG6 → YWC9YWCB → PNKJOOLK
95 cycles21 nodesZRH7iaRHA → bQI9iYQI8 → aSG7iaSG9 → bRKBiWOH8 → aQF6ibTI9 → cSLAiXNG7 → bSH6ibRG8 → cTLAiXNF7 → bSI7iaQG8 → bTK9iYOF8 → aSJ8iZPG9 → aRJ8iZPH9 → aRI7iaQH9 → bRJ8iZPH8 → aTI7iaQF9 → bRLAiXNH8 → aRG5icSH9 → dTKAiXOF6 → cTI8iZQF7 → bUKAiXOE8 → aRJ9iYPH9