Base 33: 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 → 0W → V1 → T3
317 max steps100 → 0WW → VW1 → UW2 → TW3 → SW4 → RW5 → QW6 → PW7 → OW8 → NW9 → MWA → LWB → KWC → JWD → IWE → HWF → GWG
44 max stepsH000 → GWWG → GFGH → 1WWV → V0V2
519 max steps10000 → 0WWWW → VWWW1 → V0WV2 → WSW31 → VSW32 → URW43 → TPW64 → SMW95 → RIWD6 → QDWI7 → PCWJ8 → OCWJ9 → NBWKA → MBWKB → LAWLC → M8WNB → OBWK9 → NCWJA → MAWLB
635 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 → PD1UJ8
729 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 → OH7WOF9
876 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 → LHG9MGFC
947 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 → SLG7WOGB5
10152 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 → TPE83SOI74
1171 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 → RLGB5WQLGB6