Base 38: 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 cycles12 nodes0b → a1 → Y3 → U7 → MF → 6V → OD → AR → GL → 4X → S9 → IJ
31 cycle (fixed) 1 node IbJ
44 cycles9 nodesA5VS → QHJC → E1ZO → Y9R4 → UHJ8 → M1ZG → Y5V4 → UPB8 → MDNG
52 cycles4 nodesPBbPD → QBbPC → QDbNC → PCbOD
66 cycles57 nodesC60aVQ → aPDNC2 → YD9RO4 → UIAQJ8 → MG0aLG → a64WV2 → YSOC94 → UJBPI8 → ME0aNG → a95VS2 → YQIIB4 → UEbbM8 → TN7TE9 → MK8SHG → K62YVI → WP1ZC6 → YQCOB4 → UFBPM8 → ME6UNG → O95VSE → QJ9RIC → IE0aNK → a91ZS2 → ZXII43 → WSbb86 → VT3X87 → UOKGD8 → MB3XQG → UF5VM8 → QM6UFC → OE6UNE → OA8SRE → KH9RKI → I31ZYK → YV1Z64 → YUOC74 → UNBPE8 → ME8SNG → K95VSI → QJ1ZIC → YE0aN4 → aU8S72 → YNJHE4 → U91ZS8 → YMIIF4 → U6bbU8 → VSbb87 → UT2Y88 → WMKGF6 → Q73XUC → UNDNE8 → MA8SRG → KH5VKI → Q31ZYC → YVDN64 → UP9RC8 → MICOJG
71 cycle 4 nodesSI7bTJA → UJ9bRI8 → TL8bSG9 → TKBbPH9
84 cycles93 nodesCA30aYRQ → aVHDNK62 → YPA2YRC4 → WUHCOK76 → QNC2YPEC → WED8SON6 → QKB8SQHC → KFE2YNMI → W971ZUS6 → YQNIIEB4 → UF8bbSM8 → TTF5VM89 → QLK6UHGC → OE52YWNE → WRA8SRA6 → QKHGKKHC → E432YYXO → WVT9R866 → QPLHJGCC → ED51ZWOO → YRB9RQA4 → UIHEMKJ8 → M830aYTG → aVL5VG62 → YQP4WCB4 → USFCOM98 → MJC6UPIG → OD60aVOE → aPB9RQC2 → YIFCOMJ4 → UC70aUP8 → aNMCOFE2 → YC96USP4 → UOJCOID8 → MCB0aQPG → aFD5VOM2 → YQB6UQB4 → UOFEMMD8 → MB86UTQG → OLF5VMGE → QA74WURC → SNHDNKEA → IA92YSRK → WJH1ZKI6 → YQ30aYB4 → aVUEM762 → YPN7TEC4 → UMD8SOF8 → MKB6UQHG → OF62YVME → WPA6URC6 → QOHCOKDC → ECB2YQPO → WFD9ROM6 → QIB6UQJC → OFE0aNME → aA96USR2 → YOJGKID4 → UB40aXQ8 → aTMEMF82 → YL86UTG4 → UOL4WGD8 → SMB4WQFA → SIF6UMJA → OI70aUJE → aNA0aRE2 → aYH8SK32 → YVK2YH64 → WUP2YC76 → WQNCOEB6 → QFC8SPMC → KED6UONI → OB91ZSQE → YJF9RMI4 → UI70aUJ8 → aNM0aFE2 → aY96US32 → YVOIID64 → UPAbbQC8 → TRI0aJA9 → aKH0aKH2 → aY32YY32 → YWVU6654 → URPNDCA8 → MHD9ROKG → IB62YVQK → WPF1ZMC6 → YQD6UOB4 → UOFAQMD8 → MGB6UQLG → OF64WVME → SPA6URCA → OIHCOKJE
95 cycles10 nodesUNF6bUME8 → VMG7bTLF7 → UOE5bVND8 → WNH9bRKE6 → VND5bVOE7 → WOI9bRJD6 → VNE5bVNE7 → WOH8bSKD6 → VOF6bUMD7 → VOH8bSKD7
102 cycles118 nodesGB874WUTQM → SNLF5VMGEA → QI974WUSJC → SNJE0aNIEA → aI990aSSJ2 → aYJJ0aII32 → aYV10aa632 → aZYVOC6322 → YXVPBPC644 → UTPECONC88 → MLDC8SPOGG → KDB64WVQOI → SPFB1ZQMCA → YIFD6UOMJ4 → UOB70aUQD8 → aNMFAQMFE2 → YG976UUSL4 → UONJ4WIED8 → SMB90aSQFA → aJIF6UMJI2 → YO710aaUD4 → aZUNAQE722 → YXNG8SLE44 → UTK94WSH88 → SMLJ2YIGFA → WI750aWUJ6 → aRQN0aEBA2 → aYHF8SMK32 → YVK72YUH64 → WUPN2YEC76 → WQND8SOEB6 → QKFB8SQMHC → KFE72YUNMI → WN971ZUSE6 → YQNJ8SIEB4 → UKF90aSMH8 → aMJ72YUIF2 → YWN70aUE54 → aURN8SEA72 → YNKH8SKHE4 → UK932YYSH8 → WVMJ2YIF66 → WQP70aUCB6 → aQNFCOMEB2 → YFC96USPM4 → UOJD6UOID8 → OMBB0aQQFE → aFFA6URMM2 → YOH76UUKD4 → UONB2YQED8 → WMFB8SQMF6 → QKF76UUMHC → ONE72YUNEE → WNA98SSRE6 → QKJH8SKIHC → KE330aYYNI → aVV91ZS662 → ZXPPIICC43 → WTDCbbOO86 → VTKFbbLH87 → UTGC0aPL88 → aMLD4WOGF2 → YSB74WUQ94 → USNJEMIE98 → MJ980aTSIG → aLJ60aVIG2 → aYP50aWC32 → aYVRCOA632 → YVPHBPKC64 → UPED2YONC8 → WMDB8SQOF6 → QKFB6UQMHC → OFE72YUNME → WNA96USRE6 → QOJH8SKIDC → KEB30aYQNI → aVF91ZSM62 → ZXPJ6UIC43 → WTOD0aOD86 → aQLBAQQGB2 → YGFF4WMML4 → US774WUU98 → SNNMIIFEEA → I996bbUSSK → VSLA7TRG97 → OMJH4WKIFE → SA730aYURA → aVNIGKJE62 → YP940aXSC4 → aUTJCOI872 → YNLC0aPGE4 → aUD94WSO72 → YSNJAQIE94 → UJG90aSLI8 → aMJ50aWIF2 → aYR70aUA32 → aYVNGKE632 → YVP93XSC64 → VTPJCOIC87 → OLDC0aPOGE → aDBA4WRQO2 → YSHFAQMK94 → UJG72YULI8 → WNM50aWFE6 → aRQ96USBA2 → YOJHEMKID4 → UB830aYTQ8 → aVMLEMGF62 → YP874WUTC4 → USNLCOGE98 → MJC94WSPIG → SJD60aVOIA → aPIB0aQJC2 → aYFD0aOM32 → aYVB6UQ632 → YVPOEMDC64 → UPDB7TQOC8 → NLFDAQOMGF