Base 41: 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--
23 cycles6 nodes1d → b3 → X7 → PF → 9V → LJ
31 cycle 2 nodesJeL → KeK
420 cycles10 nodesB0dU → dIL2 → b2b4 → ZW76 → TOFC → H8VO → N6XI → R4ZE → VCRA → LEPK
51 cycle 4 nodesRCeRE → SCeRD → SEePD → RDeQE
65 cycles77 nodesB93aVU → XMILI8 → P42baG → ZW8V86 → TOMHGC → H84ZWO → VO6XGA → RL7WJE → PD1cRG → bE8VQ4 → XNBSH8 → PH5YNG → T95YVC → TMGNIC → H73aXO → XQ6XE8 → RPBSFE → HD9URO → LE6XQK → RC0dSE → dGCRO2 → bF7WP4 → XP9UF8 → PL9UJG → L91cVK → bM0dI4 → dX3a72 → bXPE74 → XQATE8 → PJBSLG → H91cVO → bM6XI4 → XR3aD8 → XPDQF8 → PD9URG → LE8VQK → NC0dSI → dG4ZO2 → bV7W94 → XPLIF8 → PA2bUG → ZK8VK6 → TMeeHC → SN6XHD → RF5YPE → TD9URC → LHDQNK → D60dYS → dSEPC2 → bGATO4 → XJ7WL8 → QO1cGF → bB7WT4 → XPHMF8 → PA4ZUG → VK8VKA → NKeeJI → ML2bJJ → Z31cb6 → bYSB64 → XSGNC8 → PG6XOG → R97WVE → PMCRIG → F93aVQ → XMATI8 → PJ3aLG → X91cV8 → bPLIF4 → XA2bU8 → ZPJKF6 → TA0dUC → dKGNK2 → b6eeX4 → aY3a65 → XVRC98 → PMEPIG
73 cycles4 nodesTJ8eVLC → WJ9eUL9 → VNAeTHA → ULBeSJB
83 cycles36 nodesB983aWVU → XOMILIG8 → P842baWG → ZWO8VG86 → TON7WHGC → PH85YWNG → TO95YVGC → TMH7WNIC → PH63aYNG → XS95YVC8 → TPMFOIFC → HA93aVUO → XMK6XKI8 → RP3eeaFE → bQL1cJE4 → bXC1cS74 → bXQFOE74 → XQC8VSE8 → PNGBSOHG → H985YWVO → TOM6XIGC → RH83aWNE → XOD5YRG8 → TPE7WQFC → PHC9USNG → LG95YVOK → TM80dWIC → dOH3aNG2 → bX85YW74 → XTQNGEB8 → PIC6XSMG → RG93aVOE → XMD7WRI8 → QOE3aQGF → XCB7WTS8 → QOIFOMGF
95 cycles9 nodesWPE5eYQF9 → ZPIAeTMF6 → YPE6eXQF7 → YRJAeTLD7 → XOG7eWOG8 → XPG7eWOF8 → XPH8eVNF8 → WPG7eWOF9 → XNH8eVNH8
104 cycles43 nodesLB87eeWWTK → XWLC7WSJ88 → QOOG1cOGGF → bB887WWWT4 → XPOOHMGGF8 → PA884ZWWUG → VOOK8VKGGA → NL87eeWWJI → XWED1cRQ88 → bPOEBSQGF4 → XHCA7WUSN8 → QOKG5YOKGF → TB87eeWWTC → XWLJeeKJ88 → WWED0dRQ89 → dONEBSQHG2 → bHC85YWSN4 → XTOG5YOGB8 → TPI87WWMFC → POHA3aUNGG → XK985YWVK8 → TPOLeeIGFC → SPD72bXRFD → ZQFE9UQPE6 → TLCC9USSJC → LHGG1cOONK → b8860dYWW4 → dXSONGGC72 → bQG86XWOE4 → XROC7WSGD8 → QOGE7WQOGF → PCB87WWTSG → POIG8VOMGG → N9883aWWVI → XOOM4ZIGG8 → VP883aWWFA → XOOL9UJGG8 → PL881cWWJG → bOO91cVGG4 → bXM87WWI74 → XQPO3aGFE8 → XPCA7WUSF8 → QOKG9UOKGF