Base 40: 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--
22 cycles10 nodes2b → Y5 → SB → GN → 6X → QD → CR → EP → AT → IL
31 cycle (fixed) 1 node JdK
41 cycle (fixed) 1 node O7VG
53 cycles4 nodesQCdQE → RBdRD → SDdPC → REdOD
65 cycles33 nodesE86WVQ → QNBRGE → GC6WRO → QF7VOE → OC8URG → MF7VOI → O93ZUG → WL7VI8 → PN2aGF → YA6WT6 → SQIKDC → GD1bQO → aD7VQ4 → WOCQF8 → OE8UPG → MB7VSI → OH3ZMG → W84YV8 → UOMGFA → K95XUK → SKddIC → RL7VID → OE2aPG → YB7VS6 → SOGMFC → G95XUO → SL7VIC → OG2aNG → Y86WV6 → SQMGDC → GD5XQO → SD7VQC → OGCQNG
72 cycles19 nodesTI8dULB → VJAdSK9 → UL8dUIA → VKBdRJ9 → UK7dVJA → WLAdSI8 → VM9dTH9 → UMBdRHA → TJ9dTKB → UI9dTLA → UKAdSJA → TK8dUJB → VJ9dTK9 → UM9dTHA → UKBdRJA → TJ7dVKB → WK9dTJ8 → VN9dTG9 → UMCdQHA
84 cycles117 nodesE940cZUQ → cVLBRI82 → aNG2aNG4 → YW76WW76 → SQPOEEDC → GDB9TSQO → KHD7VQMK → OD4ddYQG → ZQI1bLD5 → aUD2aQ94 → YWLCQI76 → SPE2aPEC → YGBASSN6 → SIH6WMLC → QG52aYNE → YTC6WRA6 → SQJEOKDC → GDA0cTQO → cJD7VQK2 → aOD0cQF4 → cWD8UQ72 → aPMCQHE4 → WEB4YSP8 → UOHASMFA → KI94YULK → UL2ddaIA → bTI8ULA3 → YMJ2aKH6 → YS50cYB6 → cTSGMBA2 → aJH5XMK4 → WS50cYB8 → cTOGMFA2 → aJ95XUK4 → WSL0cIB8 → cOH2aMF2 → aY94YU54 → WUTKIA98 → OLJ1bKIG → a830caV4 → cXWMG762 → aRP5XEC4 → WSFASOB8 → OIH8UMLG → M852aYVI → YTN3ZGA6 → WSJ6WKB8 → QOH0cMFE → cC94YUR2 → aULEOI94 → WLA2aTI8 → YOJ2aKF6 → YS90cUB6 → cSLGMIB2 → aH62aXM4 → YWR4YC76 → USPEOEBA → KHB9TSMK → KH4ddYMK → ZME1bPH5 → aUB4YS94 → WULGMI98 → OL62aXIG → YR82aVC6 → YSNEOGB6 → SHA6WTMC → QJG4YNKE → UC70cWRA → cPKEOJE2 → aBA0cTS4 → cWJGMK72 → aP60cXE4 → cWRASC72 → aPIEOLE4 → WBA2aTS8 → YOJGMKF6 → S960cXUC → cRLFNIC2 → aF82aVO4 → YWN8UG76 → SPM6WHEC → QGB4YSNE → UHC6WRMA → QKF4YOJE → UC90cURA → cLKEOJI2 → aA30caT4 → cXWIK762 → aRP1bEC4 → aWFASO74 → WPI8ULE8 → OMB2aSHG → YH84YVM6 → USN4YGBA → UKH6WMJA → QK50cYJE → cTC0cRA2 → caJEOK32 → aXA0cT64 → cWRIKC72 → aPF1bOE4 → aWB8US74 → WPMGMHE8 → OB64YXSG → URH7VMCA → OKF4YOJG → U980cVUA → cNLJJIG2 → a72ddaW4 → bZT3ZA43 → YWVIK876 → SPN1bGEC → aGB6WSN4 → WQH6WMD8 → QOD4YQFE → UDC8URQA → MKFCQOJI
94 cycles21 nodesVOF6dWOF9 → XNG8dUNG7 → WPE6dWPE8 → XOIAdSLF7 → WND5dXQG8 → YPJ9dTKE6 → XPF5dXOE7 → YQJ9dTKD6 → XPG6dWNE7 → XQI8dULD7 → WPH7dVME8 → WOH7dVMF8 → WOG6dWNF8 → XOH7dVMF7 → WQG6dWND8 → XOJ9dTKF7 → WOE4dYPF8 → ZQI9dTLD5 → YQG7dVND6 → XRI9dTLC7 → WOH8dUMF8
106 cycles103 nodesC9830caVUS → cXNLFNIG62 → aR872aWVC4 → YWPNEOGE76 → SPBA6WTSEC → QJHGASNMKE → IC750cYWRM → cTPF3ZOEA2 → aWJB8USK74 → WPMH0cMHE8 → cOB54YYSF2 → aUTH8UMA94 → WMLJ4YKIH8 → UO530caYFA → cXTK8UJA62 → aRMJ0cKHC4 → cWF50cYO72 → caTP8UEA32 → aXMJASKH64 → WRI50cYLC8 → cTOF2aOFA2 → aYJ98UUK54 → WTML0cIHA8 → cOJ52aYKF2 → aYT90cUA54 → cWTLIKIA72 → aPJ31baKE4 → aXWB0cS764 → cWRPGMEC72 → aPFB5XSOE4 → WSHB8USMB8 → OMHH4YMMHG → U8554YYYVA → UTTNJJGAAA → KJJ6ddWKKK → XKCddddQJ7 → WRKJ6WKJC8 → QOF10ccOFE → cbC98UUR22 → aZMLEOIH44 → WVA52aYT88 → YTONIKGFA6 → SJ971bWUKC → aPLG0cNIE4 → cWB72aWS72 → aYPPGMEE54 → WTBB5XSSA8 → SOJHGMMKFC → G9650cYXUO → cTRL7VICA2 → aOJF2aOKF4 → YW990cUU76 → cSPLKIIEB2 → aHB31baSM4 → aXWH4YM764 → WURP4YEC98 → UOLFASOIFA → KI992aUULK → YLL2ddaII6 → bXIFddNL63 → aXMF1bOH64 → aWR94YUC74 → WUPLEOIE98 → OLBA2aTSIG → YJH82aVMK6 → YSN50cYGB6 → cTSH6WMBA2 → aQJH4YMKD4 → WUD50cYQ98 → cTOLCQIFA2 → aJE92aUPK4 → YWLB0cSI76 → cSPH2aMEB2 → aYHB4YSM54 → WUTH4YMA98 → UOLJ4YKIFA → UK930caUJA → cXLK0cJI62 → caR30caC32 → caXXEO6632 → aXRR9TCC64 → WRKFEOOJC8 → OFA90cUTOG → cLJ97VUKI2 → aOL30caIF4 → cXW92aU762 → aYRPKIEC54 → WTFB1bSOA8 → aOJH8UMKF4 → WM950cYUH8 → cTOL4YIFA2 → aUJ92aUK94 → YWLL0cII76 → cSP32aaEB2 → aYXHASM654 → WTRI4YLCA8 → UOJF2aOKFA → YK990cUUJ6 → cSLL0cIIB2 → caH32aaM32 → aYXX4Y6654 → WUTRQCCA98 → OLJFDPOKIG