Base 37: Maximum Iteration Sequences: Full Cycle

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 Max Steps Max Step Example
Full Cycle
12 max steps100
212 max steps10 → 0a → Z1 → X3T7LF5VPBDN9RHJ1ZX3
321 max steps100 → 0aa → Za1 → Ya2 → Xa3 → Wa4 → Va5 → Ua6 → Ta7 → Sa8 → Ra9 → QaA → PaB → OaC → NaD → MaE → LaF → KaG → JaH → IaIHaJIaI
422 max stepsJ000 → IaaI → IHIJ → 1aaZ → Z0Z2ZW32XS74TKF8L4VGR4VARGJAH2XKV2X6VOB6PCNCDAPOFAPMF6TMN6TEN8REJ8RIJ0ZIZ0Z2
520 max stepsI0000 → HaaaJ → JGaJI → K0aZH → aHaI1 → ZIaH2 → YHaI3 → XGaJ4 → WGaJ5 → VFaK6 → UFaK7 → TEaL8 → SEaL9 → RDaMA → QDaMB → PCaNC → OCaND → OAaPDQBaOBPEaLCOAaPD
689 max steps1000aa → aa0Z01 → aaX201 → aZU511 → ZYOB22 → XWCN44 → TSAP88 → LKELGG → 753WVU → TQMDA8 → LG8RKG → J53WVI → TQ0ZA8 → ZLFKF2 → X64VU4 → TRNC98 → LIAPIG → F4aaVM → WL8RF5 → RJ5UHA → PH1YJC → XD1YN4 → XT9Q74 → TMGJE8 → L82XSG → VK4VG6 → RP3WBA → THDMJ8 → L91YRG → XI4VI4 → TQaa98 → SR2X99 → VJHIH6 → P20ZYC → ZWCN42 → XSAP84 → TKELG8 → L73WTG → TM4VE8 → RL7SFA → LH5UJG → P51YVC → XQCNA4 → TGAPK8 → LF3WLG → T64VU8 → ROKFCA → HC4VOK → RC2XOA → VHBOJ6 → PD1YNC → XD9QN4 → TH9QJ8 → LH1YJG → X51YV4 → XTPA74 → TMELE8 → L86TSG → NK4VGE → R93WRATIGJI8L2aaXGYKBOG3VD3WN6TP9QB8LHDMJG951YVSXQIHA4TG0ZK8ZL3WF2XT5U74TPLEB8LE6TMGN84VSERK8RGAJH3WJIT20ZY8ZWKF42XS4V84TRJG98LI2XIGV4aaV6WTaa65VU2X66VPNCB6PEAPMCFD7SNMLA6TQGNG4VKER93WRA
732 max steps100007a → a70aZT1 → aZRa811 → ZZQa912 → ZXPaA32 → YWMaD43 → XUIaH64 → WRCaN95 → VNEaLD6 → UI8aRI7 → TM8aRE8 → SLCaNF9 → RG7aSKA → TIAaPI8 → SJ6aTH9 → UKAaPG7 → TK8aRG8 → SLAaPF9 → RI9aQIA → RH7aSJA → TI9aQI8 → SK7aSG9 → TJBaOH8 → SI6aTI9 → UK9aQG7 → TL9aQF8 → SKAaPG9 → RI8aRIA → SH8aRJ9 → SJ9aQH9 → RJ8aRHASH9aQJ9RJ8aRHA
886 max steps30000779 → 9772XTTS → VMMIHEE6 → P880ZSSC → ZKKCNGG2 → XB43WWP4 → USSDM887 → NKK8RGGE → J943WWRI → TSI0ZI88 → ZLJaaGF2 → YLJ1YHF3 → XV61YU54 → XTQNCA74 → TMGAPKE8 → LF83WSLG → TK64VUG8 → ROL3WFCA → THC5UOJ8 → PLC1YOFC → XDC5UON4 → TPC9QOB8 → LHEBOMJG → D851YVSO → XQKAPGA4 → TGF3WLK8 → TL63WUF8 → TOL5UFC8 → PLC5UOFC → PDC5UONC → PDC9QONC → HDC9QONK → HCA2XQOK → VGC2XOK6 → VPC3WOB6 → TPEBOMB8 → LED7SNMG → LA84VSQG → RKG4VKGA → RH43WWJA → TSH1YJ88 → XLK1YGF4 → XT63WU74USOLEC87NKC6TOGENC93WROETIC8ROI8LJBaaOHGPK71YTGCXMD3WNE4USA7SQ87NLKFKGFE9653WVUSTQOIHCA8LGC0ZOKGZC53WVO2XTQBOA74TMGCNKE8LB83WSPGTKE4VMG8RL83WSFATKH5UJG8PL41YWFCXSD5UN84TPK9QGB8LHE3WMJGT851YVS8XQLJGFA4TG62XUK8VOL3WFC6TPC5UOB8PLEBOMFCEC85USONPKC8ROGCJDC3WONITCA0ZQO8ZLGBOKF2XD63WUN4USO9QC87NKHBOJGED941YWROXSIAPI84TKEaaLG8SMD0ZNE9ZJA7SQH2XLG1YKF4XT63WU74
950 max steps100000000 → 0aaaaaaaa → Zaaaaaaa1 → Z0aaaaaZ2 → aY10aZZ21 → aZYWa3211 → ZZXUa5312 → ZXWRa8432 → YWTNaC743 → XUPGaJB64 → WRJ8aRH95 → VOI9aQIC6 → UME5aUME7 → VNG7aSKD6 → UOF6aTLC7 → UNH8aRJD7 → TME5aUME8 → VMF7aSLE6 → UOE6aTMC7 → UNH9aQJD7 → TLD5aUNF8 → VMG7aSKE6 → UOE5aUMC7 → VNI9aQID6 → UMD4aVNE7 → WOH8aRJC5 → VOF6aTLC6 → UPH8aRJB7 → TMG7aSKE8 → TLE5aUMF8 → VMF6aTLE6 → UPF6aTLB7 → UNI9aQID7 → TLD4aVNF8 → WNG7aSKD5 → VPF6aTLB6 → UPI9aQIB7 → TLF6aTLF8 → ULE5aUMF7 → VNG6aTKD6 → UPG6aTKB7 → UNI8aRID7 → TME4aVME8 → WNF7aSLD5 → VPF7aSLB6 → UOH9aQJC7 → TLE6aTMF8 → ULF6aTLF7 → UNE5aUMD7VNH8aRJD6UNE5aUMD7
1086 max steps50000055AW → WA554VVVQ5 → SQQQFKAAA9 → JGGG4VKKKI → R4440ZWWWA → ZSSSGJ8882 → XKKK2XGGG4 → VT443WWW76 → TSSPLEB888 → LKKE6TMGGG → N8543WWVSE → TSQK8RGA88 → LKJG3WKHGG → T5441YWWV8 → XSSQKFA884 → TKKG4VKGG8 → RL443WWWFA → TSSH5UJ888 → PLKK1YGGFC → XD643WWUN4 → USSO9QC887 → NKKHBOJGGE → D9441YWWRO → XSSIAPI884 → TKKEaaLGG8 → SMD4aaVNE9 → WRIE0ZMI95 → ZRI7aaSI92 → YTQA8RQA73 → VMJGFKKHE6 → P8541YWVSC → XSQKCNGA84 → TKGB3WPKG8 → TLE43WWMF8 → TSL85USF88 → PLKK5UGGFC → PD643WWUNC → TSOD9QNC88 → LKHC9QOJGG → HC541YWVOK → XSQC2XOA84 → VTKGBOKG76 → PMD43WWNEC → TSDA7SQN88 → MKKG9QKGGF → H7443WWWTK → TSSM2XE888 → VLKK7SGGF6 → PL643WWUFC → TSOD5UNC88 → PLKC9QOGFC → HDC63WUONK → TOCA2XQOC8 → VLGCBOOKF6 → PDC63WUONC → TODC9QONC8 → LHCC9QOOJG → HCC51YVOOK → XQCC2XOOA4 → VTGCBOOK76 → PMDC3WONEC → TDCA7SQON8 → MKGC9QOKGF → HC743WWTOK → TSMC2XOE88 → VLKC7SOGF6 → PLC63WUOFC → TODC5UONC8 → PLCC9QOOFC → HDCC5UOONK → PCCA2XQOOC → VGDCBOONK6 → PDCA3WQONC → TGDC9QONK8 → LHCA3WQOJG → TGC51YVOK8 → XQLC3WOFA4 → USGC5UOK87 → PNKC3WOGDC → TDCA3WQON8 → TLGC9QOKF8 → LHC63WUOJG → TOC51YVOC8 → XQLCBOOFA4 → TGDC5UONK8PLCA3WQOFCTGDC5UONK8