Base 37: 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 9 nodes1Z → X3 → T7 → LF → 5V → PB → DN → 9R → HJ
31 cycle 2 nodesHaJ → IaI
49 cycles18 nodes94VS → RIHA → H0ZK → Z2X2 → XU54 → TOB8 → LCNG → B4VQ → RELA → H6TK → N2XE → V8R6 → PIHC → D0ZO → ZAP2 → XEL4 → T6T8 → NKFE
52 cycles4 nodesOBaOD → PAaPC → QCaNB → PDaMC
66 cycles30 nodes951YVS → XQIHA4 → TG0ZK8 → ZL3WF2 → XT5U74 → TPLEB8 → LE6TMG → N84VSE → RK8RGA → JH3WJI → T20ZY8 → ZWKF42 → XS4V84 → TRJG98 → LI2XIG → V4aaV6 → WTaa65 → VU2X66 → VPNCB6 → PEAPMC → FD7SNM → LA6TQG → NG4VKE → R93WRA → TIGJI8 → L2aaXG → YKBOG3 → VD3WN6 → TP9QB8 → LHDMJG
73 cycles4 nodesQH7aSJB → TH8aRJ8 → SL9aQF9 → RJAaPHA
84 cycles44 nodes9653WVUS → TQOIHCA8 → LGC0ZOKG → ZC53WVO2 → XTQBOA74 → TMGCNKE8 → LB83WSPG → TKE4VMG8 → RL83WSFA → TKH5UJG8 → PL41YWFC → XSD5UN84 → TPK9QGB8 → LHE3WMJG → T851YVS8 → XQLJGFA4 → TG62XUK8 → VOL3WFC6 → TPC5UOB8 → PLEBOMFC → EC85USON → PKC8ROGC → JDC3WONI → TCA0ZQO8 → ZLGBOKF2 → XD63WUN4 → USO9QC87 → NKHBOJGE → D941YWRO → XSIAPI84 → TKEaaLG8 → SMD0ZNE9 → ZJA7SQH2 → XLG1YKF4 → XT63WU74 → USOLEC87 → NKC6TOGE → NC93WROE → TIC8ROI8 → LJBaaOHG → PK71YTGC → XMD3WNE4 → USA7SQ87 → NLKFKGFE
95 cycles14 nodesSLC5aUOF9 → VLG8aRKF6 → UNC4aVOD7 → WOIAaPIC5 → VMD5aUNE6 → VPH8aRJB6 → UNG7aSKD7 → TNF6aTLD8 → ULG7aSKF7 → TND4aVND8 → WNG9aQKD5 → VND6aTND6 → UPG9aQKB7 → TLF8aRLF8
109 cycles38 nodesHCCA2XQOOK → VGCC2XOOK6 → VPCC3WOOB6 → TPECBOOMB8 → LEDC7SONMG → LCA84VSQOG → RKGC4VOKGA → RHC43WWOJA → TSHC1YOJ88 → XLKC1YOGF4 → XTC63WUO74 → USOMBOEC87 → NKDC7SONGE → LCA93WRQOG → TIGC4VOKI8 → RLC3aaWOFA → XQKC2XOGA4 → VTGC3WOK76 → TPMC3WOEB8 → TLEC7SOMF8 → MKC85USOGF → PKC73WTOGC → TMDC3WONE8 → TLCA7SQOF8 → MKGC5UOKGF → PC743WWTOC → TSMDBONE88 → LKDA7SQNGG → LGA53WVQKG → TQG53WVKA8 → TQLG3WKFA8 → TLG63WUKF8 → TOL63WUFC8 → TOLC5UOFC8 → PLCC5UOOFC → PDCC5UOONC → PDCC9QOONC → HDCC9QOONK