Base 37: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
23 max steps10 → 0a → Z1 → X3
319 max steps100 → 0aa → Za1 → Ya2 → Xa3 → Wa4 → Va5 → Ua6 → Ta7 → Sa8 → Ra9 → QaA → PaB → OaC → NaD → MaE → LaF → KaG → JaH → IaI
44 max stepsJ000 → IaaI → IHIJ → 1aaZ → Z0Z2
517 max stepsI0000 → HaaaJ → JGaJI → K0aZH → aHaI1 → ZIaH2 → YHaI3 → XGaJ4 → WGaJ5 → VFaK6 → UFaK7 → TEaL8 → SEaL9 → RDaMA → QDaMB → PCaNC → OCaND → OAaPD
659 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 → R93WRA
730 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 → RJ8aRHA
882 max steps400000BY → YB3aaWP3 → XXN6TD34 → UTN9QD77 → NMH9QJEE → H981YSRK → XKI2XIG4 → VT3aaW76 → XUP1YB64 → XTODMC74 → TMC8ROE8 → LJC7SOHG → LC51YVOG → XQC4VOA4 → TRGBOK98 → LID3WNIG → TA4aaVQ8 → WSL2XF85 → VRK5UG96 → QOI3WICB → TFBaaOL8 → SPE2XMB9 → VJE7SMH6 → PL81YSFC → XKD5UNG4 → TPA3WQB8 → TLGDMKF8 → L963WURG → TOI4VIC8 → RLBaaOFA → QPC2XOBB → VFEBOML6 → PD85USNC → PKD9QNGC → HDA3WQNK → TGA2XQK8 → VLG3WKF6 → TP63WUB8 → TOLDMFC8 → LC95UROG → PIC4VOIC → RDBaaONA → QPE0ZMBB → ZFE7SML2 → XL85USF4 → TPK5UGB8 → PLE3WMFC → TD85USN8 → PLK9QGFC → HD63WUNK → TOA2XQC8 → VLGBOKF6 → PD63WUNC → TOD9QNC8 → LHC9QOJG → HC51YVOK → XQC2XOA4 → VTGBOK76 → PMD3WNEC → TDA7SQN8 → MKG9QKGF → H743WWTK → TSM2XE88 → VLK7SGF6 → PL63WUFC → TOD5UNC8 → PLC9QOFC → HDC5UONK → PCA2XQOC → VGDBONK6 → PDA3WQNC → TGD9QNK8 → LHA3WQJG → TG51YVK8 → XQL3WFA4 → USG5UK87 → PNK3WGDC → TDA3WQN8 → TLG9QKF8 → LH63WUJG → TO51YVC8 → XQLBOFA4 → TGD5UNK8
948 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 → UNE5aUMD7
1084 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 → TGDC5UONK8