Base 39: 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
25 max steps10 → 0c → b1 → Z3 → V7 → NF
320 max steps100 → 0cc → bc1 → ac2 → Zc3 → Yc4 → Xc5 → Wc6 → Vc7 → Uc8 → Tc9 → ScA → RcB → QcC → PcD → OcE → NcF → McG → LcH → KcI → JcJ
44 max stepsK000 → JccJ → JIJK → 1ccb → b0b2
521 max stepsJ0000 → IcccK → KHcKJ → L0cbI → cIcJ1 → bJcI2 → aIcJ3 → ZHcK4 → YHcK5 → XGcL6 → WGcL7 → VFcM8 → UFcM9 → TEcNA → SEcNB → RDcOC → QDcOD → PCcPE → QAcRD → SDcOB → REcNC → QCcPD
660 max steps10007b → b70bV2 → bZNE32 → ZW8T64 → VQKHC8 → NE2ZOG → XA6VS6 → RPHKDC → FC2ZQO → XE8TO6 → RL9SHC → JF3YNK → V80bU8 → bNLGF2 → Z84XU4 → VTLG98 → NK4XIG → T71aVA → ZOIJE4 → VA0bS8 → bNHKF2 → Z82ZU4 → XVLG76 → RO4XEC → TF9SNA → KI7UKJ → N20baG → bY6V42 → ZUOD84 → VMARG8 → NH5WLG → R73YVC → VOENE8 → NA8TSG → LI6VKI → P31aZE → ZWAR64 → VQGLC8 → NE4XOG → TA6VSA → PJHKJE → B2ccZS → aR6VB3 → XPFMD6 → RC6VQC → PFDONE → CA7USR → NIENKG → 971aVU → ZOKHE4 → VA2ZS8 → XNHKF6 → R82ZUC → XMENG6 → R95WTC → RKENIC → F91aTO → ZK8TI4 → VL1aH8 → ZN3YF4 → WU7U87
735 max steps400000J → J3cccYK → ZJHcKJ4 → YI0cbK5 → cWFcM61 → bWGcL62 → aVFcM73 → ZTFcM94 → YQDcOC5 → XMCcPG6 → WL8cTH7 → VOBcQE8 → UKBcQI9 → TJ7cUJA → VK9cSI8 → UM9cSG9 → TLBcQHA → SI8cTKB → UI9cSK9 → TL9cSHA → TJAcRJA → SJ7cUJB → VJ8cTJ8 → UN9cSF9 → TLCcPHA → SH7cULB → VJAcRJ8 → UL7cUH9 → VLCcPH8 → UJ7cUJ9 → VLAcRH8 → UL9cSH9 → TLAcRHA → SJ9cSJB → TH8cTLA → UJBcQJ9
8139 max stepsA0000Ebb → bbE9SO12 → aZJ9SJ33 → XWIccJ66 → WWFCPN67 → QPD7UPDD → NDCBQQPG → FEC6VQOO → PEA8TSOE → LIB9SRKI → JG31aZMK → ZW60bW64 → bVQPCC72 → ZOECPOE4 → VDA9SSP8 → NJIBQKJG → F71ccaVO → bVL6VH72 → ZPO3YED4 → WUC9SQ87 → PMJDOJGE → CA5ccWSR → XSK0bIA6 → bRI1aKB2 → aYG1aM43 → ZXU5W854 → VSRLGBA8 → NIG4XMKG → T761aWVA → ZQOIJEC4 → VEA0bSO8 → bNI9SKF2 → ZJ81aUJ4 → ZVLccG74 → YVJ9SJ75 → TOIccJEA → SOB4XREB → THG9SMLA → KI63YWKJ → VQ20baC8 → bYNDOF42 → ZUB7UR84 → VNMFMGF8 → N875WVUG → ROM6VGEC → PFA5WSNE → RIB7URKC → NGF1aNMG → Z875WVU4 → VROLGEB8 → NGA4XSMG → TI75WVKA → ROJ1aJEC → ZF9ccSN4 → YTK4XI95 → USK1aIA9 → ZLI1aKH4 → ZV41aY74 → ZVUNE874 → VOM8TGE8 → NLA5WSHG → RI73YVKC → VOF1aNE8 → ZNA7USF4 → VNI7UKF8 → OM81aUGF → ZM95WTG4 → VRK5WIB8 → RNG1aMFC → ZF85WUN4 → VRM7UGB8 → OMG5WMGF → R965WWTC → RQKENICC → FE91aTOO → ZKA8TSI4 → VLI1aKH8 → ZN41aYF4 → ZVU7U874 → VONLGFE8 → NA84XUSG → TMI6VKGA → PJ61aWJE → ZQAccRC4 → YSN0bFA5 → bTI7UK92 → ZNK1aIF4 → ZV81aU74 → ZVOLGE74 → VOA4XSE8 → TNI9SKFA → KI81aUKJ → ZM20baG4 → bYV5W742 → ZURNEB84 → VMG8TMG8 → NL65WWHG → RQ73YVCC → VOFDONE8 → NBA7USRG → NIG6VMKG → P761aWVE → ZQOAREC4 → VHE9SOL8 → NJA3YSJG → VI6ccVK8 → WUDARP87 → PMHBQLGE → FB63YWRO → VQG8TMC8 → NLE5WOHG → RA73YVSC → VOIENKE8 → NA91aTSG → ZKI6VKI4 → VP21aaD8 → ZYNBQF44 → VUF7UN88 → OMM7UGGF → N965WWTG → RQK6VICC → PFE1aONE → ZBA7USR4 → VNIFMKF8 → N871aVUG → ZOM6VGE4 → VPA5WSD8 → RNIBQKFC → GE81aUON → ZMA6VSG4 → VPI5WKD8 → RNC1aQFC → ZFE7UON4 → VNA7USF8 → OMI7UKGF → N961aWTG → ZQK6VIC4 → VPE1aOD8 → ZNC9SQF4 → VJE7UOJ8
935 max stepsJ000000TU → UTIcccJ99 → TTKAcRI9A → TJJ8cTJJA → UJ9cccSJ9 → TTJAcRJ9A → TJJ7cUJJA → VK9cccSI8 → UTKAcRI99 → TLJ8cTJHA → UJC1caQJ9 → bRI6cVKB2 → aVK8cTI73 → ZTNAcRF94 → YQJBcQJC5 → XNE6cVOF6 → WRH8cTLB7 → VOI9cSKE8 → UME5cWOG9 → XNG7cUMF6 → WQF6cVNC7 → WPJAcRJD7 → VME5cWOG8 → XOH7cULE6 → WQG6cVMC7 → WPJ9cSJD7 → VNF5cWNF8 → XOG7cUME6 → WQG7cUMC7 → VPI9cSKD8 → UMF6cVNG9 → WMF6cVNG7 → WPG6cVMD7 → WPI8cTKD7 → VOG6cVME8 → WNH7cULF7
10157 max steps40000099JU → UJ993YTTJ9 → VLKJccIIH8 → ULD30bZPH9 → bWLC3YQH62 → ZVQE3YOC74 → WUOE9SOE87 → PMJA9SSJGE → JIB5ccWRKK → XRE7ccUOB6 → WVMG2ZMG77 → XPO65WWED6 → SQQC9SQCCB → JHEEDOOOLK → BAA40bYSSS → bUIIGLKK82 → ZM521aaXG4 → ZYVS5WA744 → VUROHKEB88 → NMGA2ZSMGG → XI765WWVK6 → SQQO1aECCB → ZHEE9SOOL4 → VJAA3YSSJ8 → VNIHccKKF8 → UNE4ccXOF9 → YTJF0bNJ95 → bTK7ccUI92 → aVSC8TQA73 → XOLIDOKHE6 → RBA41aYSRC → ZUIGENMK84 → VM961aWTG8 → ZQNK5WIFC4 → VRE81aUOB8 → ZNMG9SMGF4 → VJ865WWUJ8 → RQNLccGFCC → QQCA1aSQCD → ZIEECPOOK4 → VDAA1aSSP8 → ZNIIBQKKF4 → VF821aaUN8 → ZYNM7UGF44 → VUN85WUF88 → RNMM7UGGFC → NF865WWUNG → RQM86VUGCC → PMFE5WONGE → RBA85WUSRC → RMIGENMKGC → F9661aWWTO → ZQQK8TICC4 → VLEE1aOOH8 → ZNAA3YSSF4 → WUII7UKK87 → PNM21aaGFE → ZYB85WUR44 → VURMFMGB88 → NMG75WVMGG → RO765WWVEC → RQOF9SNECC → JFEA7USONK → NIA80bUSKG → bMI71aVKG2 → aYO61aWE43 → ZXUQ9SC854 → VSMJDOJGA8 → NIB5ccWRKG → XRG92ZTMB6 → XRKG5WMIB6 → SQG61aWMCB → ZQHE5WOLC4 → VREA3YSOB8 → VNIG9SMKF8 → NJ861aWUJG → ZQM6ccVGC4 → YWNF3YNF65 → VTQ87UUC98 → OMMKDOIGGF → B9661aWWTS → ZQQKGLICC4 → VEE51aXOO8 → ZSNA9SSFA4 → VJII7UKKJ8 → OM21ccaaGF → baLK1aIH22 → aYY41aY443 → ZXUUT88854 → VSMMKHGGA8 → NI662ZWWKG → XQQ71aVCC6 → ZROEDOOEB4 → VGBA9SSRM8 → NJIG5WMKJG → R761ccaWVC → bWTK3YI962 → ZVQK1aIC74 → ZVOE1aOE74 → ZVOA9SSE74 → VOJI9SKJE8 → NJA1ccaSJG → bSK93YTIA2 → ZVKI1aKI74 → ZVO21aaE74 → ZYVO9SE744 → VUOJ9SJE88 → NMJ9ccSJGG → TMC42ZYQGA → XUJE5WOJ86 → SQM9ccSGCB → TRGC3YQMBA → VJGE5WOMJ8 → RNA5ccWSFC → XSKD3YPIA6 → VRIC1aQKB8 → ZNGE1aOMF4 → ZVA85WUS74 → VROMHKGEB8 → NGA62ZWSMG → XQI75WVKC6 → SQOE1aOECB → ZHEA9SSOL4 → VJIA3YSKJ8 → VNI1ccaKF8 → bULD2ZPH82 → ZXMC3YQG54 → WUSE5WOA87 → RPMI9SKGDC → JFC61aWQNK → ZQE80bUOC4 → bVME9SOG72 → ZOJA5WSJE4 → VRI9ccSKB8 → UTKA6VSI99 → PLKI1aKIHE → ZB421aaYR4 → ZYVUFM8744 → VUOM6VGE88 → PNMA5WSGFE → RIB85WURKC → RMGF1aNMGC → ZF865WWUN4 → VRQM7UGCB8 → OMGE5WOMGF → RA965WWTSC → RQKIENKICC → FE921aaTOO → ZYKA8TSI44 → VULI1aKH88 → ZNM41aYGF4 → ZVU85WU874 → VROMLGGEB8 → NGA64XWSMG → TQI75WVKCA → ROJE1aOJEC → ZFA9ccSSN4 → YTPD4XPD95