Base 33: 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
27 max steps10 → 0W → V1 → T3P7HF1VT3
319 max steps100 → 0WW → VW1 → UW2 → TW3 → SW4 → RW5 → QW6 → PW7 → OW8 → NW9 → MWA → LWB → KWC → JWD → IWE → HWF → GWGFWHGWG
49 max stepsH000 → GWWG → GFGH → 1WWV → V0V2VS32TO74PGF8H0VGV0V2
520 max steps10000 → 0WWWW → VWWW1 → V0WV2 → WSW31 → VSW32 → URW43 → TPW64 → SMW95 → RIWD6 → QDWI7 → PCWJ8 → OCWJ9 → NBWKA → MBWKB → LAWLC → M8WNB → OBWK9 → NCWJA → MAWLBMAWLB
639 max steps10007G → G70VPH → VI0VE2 → VT3S32 → TQO764 → PKGFC8 → H80VOG → VG0VG2 → VSWW32 → UT2T33 → SQP665 → NKIDCA → D84ROK → NG6PGA → JCWWJE → KHWWED → JI2TEE → R53SR6 → PMKBA8 → HC8NKG → F80VOI → VG2TG2 → TQWW54 → SR2T55 → RNLA96 → LEALIC → B93SNM → PEALI8 → HB3SLG → PA0VM8 → VHBKF2 → T91UN4 → TPDI74 → PI4RE8 → NH3SFA → PD1UJ8TH5QF4PL1UB8TH9MF4PD1UJ8
731 max stepsA0000OO → OO9WM89 → OFEWHH9 → NA1WUMA → VKCWJC2 → UJ7WOD3 → TNAWL94 → SKCWJC5 → RG7WOG6 → QK7WOC7 → PJBWKD8 → OE6WPI9 → QG9WMG7 → PH5WQF8 → RI9WME6 → QI7WOE7 → PJ9WMD8 → OG8WNG9 → OF6WPH9 → QG8WNG7 → PI6WPE8 → QHAWLF7 → PG5WQG8 → RI8WNE6 → QJ8WND7 → PI9WME8 → OG7WOG9 → PF7WOH8 → PH8WNF8 → OH7WOF9PF8WNH8OH7WOF9
894 max steps70000DRR → RRD6PJ56 → MLJ5QDBB → LBA5QMLC → LCA8NMKC → FC97ONKI → HE82TOIG → RG40VSG6 → VOKWWB82 → UOK3SC83 → RPG7OG76 → LIGWWFEC → KI61UQED → TK73SPC4 → QOI7OE87 → JHG3SGFE → P51WWUR8 → VRM1UA52 → USMBKA43 → ROC8NK86 → LGF7OHGC → H91WWUNG → VNE5QI92 → TLE3SIB4 → QOA3SM87 → PJGBKGD8 → H95WWQNG → RNA5QM96 → MKEBKICB → B983SONM → PGEALIG8 → HB3WWSLG → TLC3SKB4 → QOA7OM87 → JHGBKGFE → 951WWURO → VRL2TB52 → TRM9MA54 → PMDBKJA8 → HC95QNKG → LE80VOIC → VG93SNG2 → TPDWWI74 → SPG6PG75 → NJHWWEDA → MJ91UNDB → TEB5QLI4 → PLA3SMB8 → PHC9MKF8 → HD81UOJG → TG60VQG4 → VPJWWC72 → UPJ5QD73 → RLI5QEB6 → MKA3SMCB → PCB7OLK8 → IGA7OMGF → HC2WWTKG → UKD2TJC3 → SQ85QO65 → NLKFGCBA → DA80VOMK → VGC6PKG2 → TJ7WWOD4 → SPG4RG75 → OMHWWEA9 → NMA4RMAA → NDCBKKJA → D985QONK → LGE6PIGC → J93WWSNE → TNE3SI94 → QOE3SI87 → PJG3SGD8 → PH5WWQF8 → ROB7OL86 → LHG9MGFCD91WWUNKVNH2TF92TRE1UI54TPM3SA74QOIBKE87JG93SNGEPE4WWRI8SOD6PJ85NJG5QGDALD5WWQJCRKD1UJC6TL85QOB4PLG9MGB8HD9WWMJGNJ61UQDATKD5QJC4PL85QOB8LHG9MGFC
949 max stepsC00000000 → BWWWWWWWL → LAWWWWWLC → MKBAWLLCB → MBA8WNMLB → ODBAWLLJ9 → NEA7WOMIA → PED7WOJI8 → PHB4WRLF8 → SJE5WQID5 → RND4WRJ96 → SLI9WMEB5 → RJB6WPLD6 → QLE7WOIB7 → PJD6WPJD8 → QHC5WQKF7 → RJE4WRID6 → SLE4WRIB5 → SNG6WPG95 → RMG6WPGA6 → QLF5WQHB7 → RJF5WQHD6 → RLD3WSJB6 → TMG7WOGA4 → SME5WQIA5 → RNG7WOG96 → QKF6WPHC7 → QJD4WRJD7 → SKD5WQJC5 → RNE6WPI96 → QLG8WNGB7 → PIC4WRKE8 → SJD5WQJD5 → RND5WQJ96 → RLH9WMFB6 → QIB5WQLE7 → RJF6WPHD6 → QLC3WSKB7 → TLF8WNHB4 → SLC5WQKB5 → RNF8WNH96 → QJE7WOID7 → PJB4WRLD8 → SJE7WOID5 → RLB4WRLB6 → SLG9WMGB5 → RJB4WRLD6 → SLG7WOGB5RLD4WRJB6SLG7WOGB5
10245 max steps5000000AAO → OAA4WWRMM9 → SNHDWWIF95 → RNF80VOH96 → VLGE1UIGB2 → USA3WWSM43 → TTQI5QE634 → QPLK3SCB77 → PJIA7OMED8 → IGC63SQKGF → PK82WWTOC8 → UOLD3SJB83 → RPGA5QMG76 → MKIBWWKECB → LLA61UQMBC → TKCA8NMKC4 → PFC87OOKH8 → IGG81UOGGF → TG2WWWWTG4 → USGFWWGG43 → TSFBWWKH44 → SSID2TJE45 → RON63SQ986 → PLKGDIGCB8 → HA84WWROMG → SOH84ROF85 → OMGG1UGGA9 → TFBWWWWKH4 → SLHF8NHFB5 → NFA21UUMHA → TSDC1UKJ44 → TPO85QO874 → PLIGFGGEB8 → HA40WWVSMG → WSLC4RKB41 → VONA7OM982 → THGEBKIGF4 → P941WWUSN8 → VSMJ1UDA42 → USOC5QK843 → ROLG7OGB86 → LHG9WWMGFC → NK750VRPCA → VMID7OJEA2 → THC63SQKF4 → QOK81UOC87 → TJGG7OGGD4 → PH5WWWWQF8 → ROHF0VHF86 → VLG21UUGB2 → USS9WWM443 → TSQJ5QD644 → POLK5QCB88 → LHGA7OMGFC → HC91WWUNKG → VNI72TPE92 → TRIE3SIE54 → QOM43SSA87 → POJGBKGD88 → HG95WWQNGG → RNA70VPM96 → VLIEBKIEB2 → TA943SSNM4 → QOOEBKI887 → JGG93SNGGE → PE4WWWWRI8 → SOIE1UIE85 → TNG43SSG94 → QOODWWI887 → POIB5QLE88 → LHGA3SMGFC → PC91WWUNK8 → VOLD2TJB82 → TRGA5QMG54 → PMLBWWKBA8 → OMEB0VLIA9 → VFCA3SMKH2 → TPC81UOK74 → TPIG7OGE74 → PIH3WWSFE8 → TOEA0VMI84 → VPGC3SKG72 → TPI7WWOE74 → SPMB5QLA75 → NLIC9MKEBA → ECA83SOMKJ → PGC84ROKG8 → NHG7WWOGFA → PM970VPNA8 → VIHEBKIFE2 → T9441USSN4 → TPOODI8874 → PIGG4RGGE8 → NH3WWWWSFA → TMHF4RHFA4 → PNC21UUK98 → TSHE7OIF44 → POH41USF88 → TOHG1UGF84 → TPG1WWUG74 → VSND8NJ942 → TOFE5QIH84 → PLG41USGB8 → TOH9WWMF84 → SOK94RNC85 → OMGE7OIGA9 → HFC3WWSKHG → TKD3WWSJC4 → TSHF0VHF44 → VPO21UU872 → USSIFGE443 → ROO40VS886 → VOLGFGGB82 → TGA0WWVMG4 → WSLD5QJB41 → VOLA5QMB82 → TLGC9MKGB4 → PDA7WWOMJ8 → POFB2TLH88 → RHGA1UMGF6 → TLC1WWUKB4 → VSJH0VFD42 → VTO61UQ832 → USQKFGC643 → ROK80VOC86 → VLGG7OGGB2 → TH9WWWWMF4 → SNHF6PHF95 → NJE21UUIDA → TSD63SQJ44 → QOOK5QC887 → LJGG7OGGDC → H95WWWWQNG → RNGF2THG96 → RLE1WWUIB6 → VQJD2TJD62 → TRK65QQC54 → PMLK7OCBA8 → IGCA7OMKGF → HC82WWTOKG → UOH82TOF83 → SQGG1UGG65 → TNJWWWWC94 → SNKD5QJC95 → NLE85QOIBA → LGDA3SMJGC → PC95WWQNK8 → ROHD2TJF86 → RLG61UQGB6 → TLK9WWMCB4 → SNIA0VME95 → VNEC3SKI92 → TPE83SOI74QOIG3SGE87PJG3WWSGD8TOF92TNH84RPGE1UIG76TLI3WWSEB4TSIE2TIE44RPO43SS876POLIFGEB88HGA40VSMGGVOC0WWVK82WUNJ3SD921VSPE5QI742TOLI3SEB84QOGA3SMG87PJGBWWKGD8OLC42TSKB9ROFA7OMH86LHGC1UKGFCT981WWUON4VSMK0VCA42VTOC7OK832TQHG7OGF64PKH1WWUFC8VOIA2TME82TRGC3SKG54QOM7WWOA87PPIE1UIE78TIH43SSFE4QOO41US887TOJGFGGD84PG60WWVQG8WQNA8NM961VKFEBKIHC2T9841USON4TPOGDIG874PIG4WWRGE8SOD91UNJ85TNGE5QIG94PLE3WWSIB8TOHB2TLF84RPGA1UMG76TLIBWWKEB4SLI71UPEB5TNIA3SME94QOEC3SKI87PJG83SOGD8PHG5WWQGF8ROB90VNL86VLGE9MIGB2TDA3WWSMJ4TSJF2THD44RPO61UQ876TLKIFGECB4PA840VSOM8VOHGBKGF82TG91WWUNG4VSLD6PJB42TOJA5QMD84PLGC5QKGB8LHA7WWOMFCPMC73SPKA8PIHC7OKFE8IG841USOGFTOG2WWTG84USLD7OJB43ROHA5QMF86MKGC1UKGCBTB87WWOOL4SPLD2TJB75RNIA5QME96MKEC3SKICBPB883SOOL8PHGG9MGGF8HD1WWWWUJGVJGFALHGD2TB61WWUQL4VSOI4RE842TONG3SG984QOGDWWIG87POD81UOJ88THGG5QGGF4PL1WWWWUB8VOLB4RLB82TNGA9MMG94PEDBWWKJI8OLC60VQKB9VKFA7OMHC2THC81UOKF4TPG81UOG74TPIFWWGE74SPFA1UMH75TNIC1UKE94TPE83SOI74
11106 max steps70000009GGT → TGG96WPNGG4 → SNG6WWWPG95 → RQNC8WNK966 → QLIEAWLIEB7 → PGA73WSPMG8 → TLHF5WQHFB4 → SOF61WUQH85 → VPMI8WNEA72 → UOHD7WOJF83 → TNGB3WSLG94 → TPJC4WRKD74 → SPKD6WPJC75 → RMID6WPJEA6 → QLF94WRNHB7 → SKHC5WQKFC5 → RNE84WROI96 → SLJF8WNHDB5 → RKC83WSOKC6 → TMJC7WOKDA4 → SMEA6WPMIA5 → RMFC7WOKHA6 → QKEA4WRMIC7 → SKGA5WQMGC5 → RNGA3WSMG96 → TMID5WQJEA4 → SOG94WRNG85 → SNJF6WPHD95 → RMGA3WSMGA6 → TMHC5WQKFA4 → SOGA4WRMG85 → SNJE5WQID95 → RNHA4WRMF96 → SLID6WPJEB5 → RME84WROIA6 → SLJE7WOIDB5 → RLD84WROJB6 → SLJD7WOJDB5 → RLD85WQOJB6 → RLID7WOJEB6 → QKD84WROJC7 → SKIC6WPKEC5 → RMD85WQOJA6 → RLIE8WNIEB6 → QJC73WSPKD7 → TLJD6WPJDB4 → SNE85WQOI95 → RNIF8WNHE96 → QJE92WTNID7 → UMHA4WRMFA3 → TQHC6WPKF64 → SNKD4WRJC95 → SNIB6WPLE95 → RMGC6WPKGA6 → QLFA3WSMHB7 → TLGB5WQLGB4 → SOFA4WRMH85 → SNJE6WPID95 → RMGA4WRMGA6 → SLHC5WQKFB5 → RNF94WRNH96 → SLIE7WOIEB5 → RLD73WSPJB6 → TMKE7WOICA4 → SMEA5WQMIA5 → RNGC7WOKG96 → QKFB3WSLHC7 → TLF94WRNHB4 → SPIC5WQKE75 → RNJD5WQJD96 → RLHA5WQMFB6 → RLGB5WQLGB6RLFA4WRMHB6SLHB5WQLFB5RNFA5WQMH96RLHD6WPJFB6QLE83WSOIB7TLID6WPJEB4SNE84WROI95SNJF8WNHD95RKEA3WSMIC6TMHA5WQMFA4SOGC6WPKG85RMHC3WSKFA6TMHA4WRMFA4SPHC6WPKF75RMID4WRJEA6SLH94WRNFB5SNIC5WQKE95RNHB5WQLF96RLHC5WQKFB6RLF94WRNHB6SLIC5WQKEB5RNF95WQNH96RLHE7WOIFB6QKD72WTPJC7UMJD6WPJDA3TOF95WQNH84SOIF7WOHE85RLGA2WTMGB6UNHB4WRLF93TQIC5WQKE64SOKE5WQIC85RNIC5WQKE96RLHB5WQLFB6RLFA5WQMHB6RLGB5WQLGB6