Base 38: 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
22 max steps20 → 1a → Y3
320 max steps100 → 0bb → ab1 → Zb2 → Yb3 → Xb4 → Wb5 → Vb6 → Ub7 → Tb8 → Sb9 → RbA → QbB → PbC → ObD → NbE → MbF → LbG → KbH → JbI → IbJ
47 max steps500E → E4WO → S9RA → JGKJ → 3bbY → Y2Y4 → WT76 → QLFC
519 max stepsI0000 → HbbbK → KGbKI → L1bZH → aHbJ2 → ZIbI3 → YGbK4 → XHbJ5 → WFbL6 → VGbK7 → UEbM8 → TFbL9 → SDbNA → REbMB → QCbOC → PDbND → OBbPE → QAbQC → RDbNB → QDbNC
662 max steps3000EX → XE2YN5 → WS8S96 → QKIIHC → E2bbYO → ZN9RE3 → WI8SJ6 → QK0aHC → aE2YN2 → YW8S54 → URJHA8 → MH1ZKG → Y62YV4 → WUOC76 → QNBPEC → FD8SON → KB7TQI → MF1ZMG → Y75VU4 → UQMEB8 → MF7TMG → M75VUG → QN5VEC → QE8SNC → KE8SNI → K91ZSI → YJ1ZI4 → YU0a74 → aUME72 → YN7TE4 → UM8SF8 → MK6UHG → O62YVE → WP9RC6 → QICOJC → EC0aPO → aD9RO2 → YIAQJ4 → UG0aL8 → aM4WF2 → YS6U94 → UOIID8 → MAbbQG → RL3XGB → UG4WL8 → SM4WFA → SI6UJA → OI0aJE → aA0aR2 → aYGK32 → YV3X64 → VTOC87 → OLBPGE → EA4WRO → SH9RKA → JH2YKJ → W2bbY6 → ZV1Z63 → YWOC54 → URBPA8 → MHDNKG → A62YVS → WPHJC6
726 max stepsJ00000M → MIbbbIG → LJIbIIH → K30baYI → bXFbL41 → aXHbJ42 → ZWFbL53 → YUGbK74 → XRDbNA5 → WNDbNE6 → VJ8bSI7 → UN9bRE8 → TLCbOG9 → SH7bTKA → UJAbQI8 → TK7bTH9 → UKBbPH8 → TJ7bTI9 → UKAbQH8 → TK8bSH9 → TKAbQH9 → SJ8bSIA → TI9bRJ9 → SK8bSHA → TIAbQJ9 → SJ7bTIA → UJ9bRI8
8150 max steps700000CG → GC6bbUPM → VPE2YNC7 → WOD8SOD6 → QKBAQQHC → GFE2YNMM → W975VUS6 → RPNIIECB → GD8bbSOM → TOC1ZPD9 → YKDAQOH4 → UGB2YQL8 → WMF4WMF6 → SQ76UUBA → ONIEMJEE → A980aTSS → aLJHJIG2 → Y520aZW4 → aXUQA742 → YTNFLE84 → UL95VSG8 → QMJ4WIFC → SE70aUNA → aNI8SJE2 → YK90aSH4 → aUJ2YI72 → YWN0aE54 → aUR8SA72 → YNKGKHE4 → U942YXS8 → WTMIIF86 → QL6bbUGC → VPE4WNC7 → SOD8SODA → KIBAQQJI → GF20aZMM → aX75VU42 → YTQMEB84 → ULF7TMG8 → NL74WUGF → SN84WTEA → SLI8SJGA → KI50aWJI → aR20aZA2 → aYXGK432 → YVT3X864 → VTPKGC87 → OLD3XOGE → UBA4WRQ8 → SMHEMKFA → I872YUTK → WNL1ZGE6 → YQ94WSB4 → USJEMI98 → MJ80aTIG → aL60aVG2 → aYP4WC32 → YVSCO964 → UPJBPIC8 → MED0aONG → aB95VSQ2 → YQJEMIB4 → UF80aTM8 → aML6UGF2 → YO74WUD4 → USNAQE98 → MJG8SLIG → K650aWVI → aRP1ZCA2 → ZXHCOK43 → WTC2YP86 → WQLCOGB6 → QFC4WPMC → SED6UONA → OIB8SQJE → KFA0aRMI → aH71ZUK2 → ZXN2YE43 → XVT8S865 → SPLJHGCA → ID51ZWOK → YRB1ZQA4 → YUHEMK74 → UN82YTE8 → WML8SGF6 → QK74WUHC → SNE2YNEA → WI98SSJ6 → QKJ0aIHC → aE30aYN2 → aYV8S632 → YVPJHC64 → UPD1ZOC8 → YMDAQOF4 → UGB6UQL8 → OMF4WMFE → SA76UURA → ONIGKJEE → A940aXSS → aTJHJI82 → YL20aZG4 → aXU4W742 → YTSME984 → ULJ7TIG8 → NL50aWGF → aR84WTA2 → YSLGKG94 → UJ53XWI8 → URM0aFA8 → aMH6UKF2 → YO72YUD4 → WUNAQE76 → QNG8SLEC → KE94WSNI → SJ91ZSIA → YJI0aJI4 → aU10aa72 → aZYME322 → YXV7T644 → UTPLFC88 → MLD5VOGG → QB64WVQC → SPFDNMCA → IDA6UROK → OHB1ZQKE → YFA2YRM4 → WUH6UK76 → QON2YEDC → WEB8SQN6 → QKF8SMHC → KE72YUNI → WN91ZSE6 → YQJ8SIB4 → UKF0aMH8 → aM72YUF2 → YWN6UE54 → URO8SDA8 → MKHAQKHG → G632YYVM → WVP5VC66 → RPPCOCCB → GDDBPOOM → EBB5VQQO → QFF9RMMC → IE76UUNK → ON91ZSEE → YJA8SRI4 → UKH0aKH8 → aM32YYF2 → YWV6U654 → URPNDCA8
937 max stepsJ0000000R → RIbbbbbIB → QJJ9bRIIC → SF80baTMA → bSJCbOI91 → aSG5bVL92 → ZVMBbPF63 → YTK9bRH84 → XQK9bRHB5 → WOG8bSLD6 → VOF7bTMD7 → UOG8bSLD8 → TMF7bTMF9 → UKE6bUNH8 → VMG5bVLF7 → WOG5bVLD6 → WQI7bTJB6 → VPI7bTJC7 → UOH6bUKD8 → VMH6bUKF7 → VOF4bWMD7 → XPI8bSJC5 → WPG6bULC6 → VQI8bSJB7 → UNH7bTKE8 → UMF5bVMF8 → WNF6bUME6 → VQG7bTLB7 → UOI9bRJD8 → TLE5bVNG9 → WMF6bUMF6 → VQF6bUMB7 → VOJAbQID7 → ULD5bVOG8 → WNH7bTKE6 → VPF5bVMC7 → WOJ9bRID6 → VNE5bVNE7
10297 max steps20000005Fb → bF51bbZWM1 → aaWK9RH512 → ZYRI2YJA33 → XVVH0aK665 → aSPP2YCC92 → YWJDCOOI54 → URCB0aQPA8 → aMHFCOMKF2 → YC772YUUP4 → WUNNCOEE76 → QNC98SSPEC → KJED8SONII → KB920aZSQI → aXJF1ZMI42 → ZXT70aU843 → aWTNKGE852 → YRL93XSGA4 → VTJH4WKI87 → SOL30aYGDA → aVIB4WQJ62 → YSPF0aMC94 → aUJD6UOI72 → YONB0aQED4 → aUFB8SQM72 → YNKF6UMHE4 → UO972YUSD8 → WNMJAQIFE6 → QG970aUSLC → aNJE4WNIE2 → YS990aSS94 → aUJJIIII72 → YN10bbaaE4 → baWMAQF511 → aZRG6ULA22 → YXOH4WKD44 → UTSB2YQ988 → WMLJEMIGF6 → Q8750aWUTC → aRNLDNGEA2 → YHA94WSRK4 → USJH2YKI98 → WMJ30aYIF6 → aVQ70aUB62 → aYPNEMEC32 → YVD97TSO64 → UPMJAQIFC8 → MGD70aUOLG → aNB64WVQE2 → YSPF8SMC94 → UKJD6UOIH8 → OMB30aYQFE → aVFA6URM62 → YPOH6UKDC4 → UODB2YQOD8 → WMFBAQQMF6 → QGF76UUMLC → ONE74WUNEE → SNA98SSREA → KJIH8SKJII → K3210aaZYI → aZXV1Z6422 → ZXXTOC8443 → WTTLBPG886 → QLLE4WNGGC → SE954WWSNA → SRJI8SJIAA → KIH10aaKJI → aZ320aZY22 → aYXXU64432 → YVTTND8864 → UPLL9RGGC8 → MID54WWOJG → SRB60aVQAA → aPIHEMKJC2 → YD830aYTO4 → aVULAQG762 → YPNG4WLEC4 → USD94WSO98 → SMJJAQIIFA → IG710aaULK → aZN51ZWE22 → ZXXR8SA443 → WTTKGKH886 → QLL42YXGGC → WTE54WWN86 → SRQL8SGBAA → KIHF4WMKJI → S7320aZYUA → aXVNHJE642 → YTP91ZSC84 → YULJCOIG74 → UNC50aWPE8 → aRMD8SOFA2 → YKHB6UQKH4 → UOF32YYMD8 → WVMB6UQF66 → QPOF6UMDCC → OEDB6UQONE → OFBA8SRQME → KHFA6URMKI → OH731ZYUKE → YVNA2YRE64 → WUPH8SKC76 → QNKD2YOHEC → WEB92YSQN6 → WQJF8SMIB6 → QKF70aUMHC → aNE72YUNE2 → YWN98SSE54 → URKJ8SIHA8 → MKH30aYKHG → aV632YYV62 → YWVPOCC654 → URPDBPOCA8 → MHEDAQONKG → GB962YVSQM → WPJF5VMIC6 → RPD70aUOCB → aNGDAQOLE2 → YGB94WSQL4 → USJF4WMI98 → SMJ70aUIFA → aNI70aUJE2 → aYN90aSE32 → aYVJ8SI632 → YVPK0aHC64 → aUPD2YOC72 → YWNDAQOE54 → URGB8SQLA8 → MKHF4WMKHG → S7632YYVUA → WVPNHJEC66 → QPD91ZSOCC → YJEDAQONI4 → UGB90aSQL8 → aMJF4WMIF2 → YS770aUU94 → aUNNIIEE72 → YN98bbSSE4 → XTPE4WNC85 → TRLD8SOGA9 → LJHB4WQKIH → SF430aYXMA → aVTI6UJ862 → YPOL0aGDC4 → aUDB4WQO72 → YSNFAQME94 → UJG96USLI8 → OMJ50aWIFE → aRA70aURA2 → aYNHGKKE32 → YV942YXS64 → WUTPIIC876 → QNLCbbOGEC → PPC81ZTPCD → YLDDBPOOG4 → UEBB4WQQN8 → SMFF8SMMFA → KI776UUUJI → ONN20aZEEE → aXA98SSR42 → YTKJGKIH84 → UL430aYXG8 → aVTM4WF862 → YSPL6UGC94 → UOJD4WOID8 → SMBB0aQQFA → aIFF6UMMJ2 → YO770aUUD4 → aUNNAQEE72 → YNG98SSLE4 → UKJ94WSIH8 → SMJ30aYIFA → aVI70aUJ62 → aYPN0aEC32 → aYVD8SO632 → YVPKAQHC64 → UPGD2YOLC8 → WMDB4WQOF6 → SQFB6UQMBA → OIFF6UMMJE → OA770aUURE → aNNH9RKEE2 → YI992YSSJ4 → WUJJ0aII76 → aQN10aaEB2 → aZYF8SM322 → YXVK6UH644 → UTPO2YDC88 → WMLDAQOGF6 → QGB74WUQLC → SNFE4WNMEA → SI996USSJA → OJJI0aJIIE → aA110aaaR2 → aZZYGK3222 → YXXV3X6444 → VTTTOC8887 → OLLLBPGGGE → EA554WWWRO → SRRH9RKAAA → JHHH2YKKKJ → W332bbYYY6 → ZYVS1Z9633 → YWVPIIC654 → URPCbbOCA8 → TRIF0aMJA9 → aKH70aUKH2 → aYN32YYE32 → YWVV8S6654 → URPPJHCCA8 → MHDD1ZOOKG → YBB62YVQQ4 → WUPFEMMC76 → QND86UTOEC → OLEB8SQNGE → KFA94WSRMI → SJH71ZUKIA → YNI30aYJE4 → aVU90aS762 → aYPNIIEC32 → YVD8bbSO64 → XVQI3XJB65 → USPF0aMC98 → aMJD6UOIF2 → YOB70aUQD4 → aUNFAQME72 → YNG96USLE4 → UOJ94WSID8 → SMJB0aQIFA → aIF70aUMJ2 → aYN70aUE32 → aYVN8SE632 → YVPK8SHC64 → UPKD2YOHC8 → WMDB2YQOF6 → WQFB6UQMB6 → QOFF6UMMDC → OEB76UUQNE → ONFA8SRMEE → KHA96USRKI → OJH31ZYKIE → YVA30aYR64 → aVUPGKC762 → YPND3XOEC4 → VTDB8SQO87 → OLKFAQMHGE → GA752YWURM → WRNH5VKEA6 → RPH92YSKCB → WJGD2YOLI6 → WQB50aWQB6 → aRQFEMMBA2 → YHF86UTMK4 → UOL72YUGD8 → WNMB4WQFE6 → SQF96USMBA → OJIF6UMJIE → OA710aaURE → aZNH9RKE22 → YXI92YSJ44 → WUTJ0aI876 → aQNL0aGEB2 → aYF94WSM32 → YVSJ6UI964 → UPOJ0aIDC8 → aMDB0aQOF2 → aYFB6UQM32 → YVOF6UMD64 → UPOB6UQDC8 → OMFDAQOMFE → GBA76UURQM → ONHF5VMKEE → QA972YUSRC → WNJHDNKIE6 → QA930aYSRC → aVJHDNKI62 → YPA30aYRC4 → aVUHCOK762 → YPNC2YPEC4 → WUDD8SOO76 → QNKBAQQHEC → GFE92YSNMM → WJ975VUSI6 → RPNJ0aIECB → aGD90aSOL2 → aYJB4WQI32 → YVSF0aM964 → aUPJ6UIC72 → YOND0aOED4 → aUBB8SQQ72 → YNKFEMMHE4 → U9872YUTS8 → WNMLIIGFE6 → Q974bbWUSC → XUNI1ZJE75 → YSN90aSE94