Base 29: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV

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 steps1 → 0 → 0
27 max steps10 → 0S → R1 → P3 → L7 → DF → 1R → P3
317 max steps100 → 0SS → RS1 → QS2 → PS3 → OS4 → NS5 → MS6 → LS7 → KS8 → JS9 → ISA → HSB → GSC → FSD → ESE → DSF → ESE
418 max stepsF000 → ESSE → EDEF → 1SSR → R0R2 → RO32 → PK74 → LCF8 → D2PG → N2P6 → NGB6 → H4NC → J4NA → J8JA → B8JI → B6LI → F6LE → F0RE → R0R2
519 max steps30000 → 2SSSQ → Q1SQ3 → RMS52 → QLS63 → PJS84 → OGSB5 → NCSF6 → MASH7 → LBSG8 → K9SI9 → JASHA → I8SJB → K7SK9 → LASH8 → KASH9 → J9SIA → J8SJA → K8SJ9 → KASH9
6105 max stepsB000PP → PPAH34 → ML6L77 → GEDEED → 30SSRQ → SP0R31 → SQL621 → ROED42 → PK0R84 → RLBG72 → PE4NE4 → LISS98 → KJ2P99 → NB9IH6 → H95MJC → HA4NIC → J84NKA → JC8JGA → B93OJI → LA6LI8 → FD7KFE → D20RQG → RO2P42 → PNJ854 → LIAHA8 → D86LKG → FC2PGE → N40RO6 → RKGB82 → PC4NG4 → LJ3O98 → LD9IF8 → D91QJG → PA2PI4 → NL7K76 → HECFEC → 52SSPO → QN0R53 → RNHA52 → PI6LA4 → LF7KD8 → EC1QGF → P40RO4 → RLJ872 → PEAHE4 → L6SSL8 → MJSS87 → LK2P88 → NDBGF6 → H51QNC → PI4NA4 → LJ7K98 → EC9IGF → 940ROK → RKAH82 → PC6LG4 → LF3OD8 → LD1QF8 → PD1QF4 → PL1Q74 → PLDE74 → LE0RE8 → RCSSF2 → QGBGC3 → N53ON6 → LIGBA8 → D84NKG → JC2PGA → N93OJ6 → LH9IB8 → D95MJG → HA2PIC → N84NK6 → JHBGBA → 964NMK → JGAHCA → 973OLK → LEAHE8 → D6SSLG → MF4ND7 → JF1QDA → P91QJ4 → PL9I74 → LE8JE8 → DASSHG → IF0RDB → R71QL2 → QODE43 → NK0R86 → RHBGB2 → P64NM4 → LJFC98 → DA2PIG → N82PK6 → NHBGB6 → H64NMC → JG4NCA → J93OJA → LA8JI8 → DB7KHG → D62PMG → NG2PC6 → NH3OB6 → LH5MB8 → HD5MFC → H51QNC
729 max stepsE0000EK → KEDSEE9 → J6SSSLA → MI8SJA7 → LE8SJE8 → KD4SNF9 → OE6SLE5 → NI6SLA6 → MHASHB7 → LC5SMG8 → NE8SJE6 → MF4SND7 → OG8SJC5 → NG6SLC6 → MH8SJB7 → LE7SKE8 → LD5SMF8 → NE7SKE6 → MG5SMC7 → NF9SID6 → ME4SNE7 → OG7SKC5 → NH7SKB6 → MG8SJC7 → LE6SLE8 → MD6SLF7 → MF7SKD7 → LF6SLD8 → MD7SKF7 → LF6SLD8
877 max steps200003EQ → QE31QPE3 → PNLSS654 → ONJ1Q955 → PJI9IA94 → LA97KJI8 → ECA7KIGF → D840ROKG → RKC2PG82 → PNC3OG54 → MKI3OA87 → LFC7KGD8 → EC41QOGF → PK40RO84 → RLKBG872 → PEC4NGE4 → LJ3SSO98 → PKF1QD84 → PLC1QG74 → PLE3OE74 → MKDSSE87 → LK95MJ88 → HDC9IGFC → 9541QONK → PKIAHA84 → LC86LKG8 → FDC3OGFE → L420RQO8 → ROKCF842 → PKC2PG84 → NLC3OG76 → LHE3OEB8 → LD5SSMF8 → NK95MJ86 → IGC9IGCB → 9743OOLK → LKEAHE88 → DC6SSLGG → MG7SSKC7 → LLA3OI78 → LED7KFE8 → EC1SSQGF → RGC0RGC2 → RP43OO32 → PMLJ8764 → LGEAHEC8 → D73SSOLG → PLB4NH74 → LJE5ME98 → HD9SSIFC → JG51QNCA → PI93OJA4 → MKA7KI87 → FDC7KGFE → D420RQOG → ROK2P842 → PNKBG854 → LIC4NGA8 → JD83OKFA → LC91QJG8 → PDA3OIF4 → MK81QK87 → PFCBGGD4 → L541QON8 → PKICFA84 → LC82PKG8 → NDC3OGF6 → LH41QOB8 → PKD5MF84 → LHC1QGB8 → PD63OMF4 → MKG1QC87 → PFC3OGD4 → MK41QO87 → PKFBGD84 → LC51QNG8 → PID3OFA4 → MK81QK87
958 max steps80000000S → S7SSSSSK1 → RL7SSSK72 → QLL6SL773 → PKEDSEE84 → OH6SSSLB5 → NMH6SLB66 → MHG9SICB7 → LD74SNLF8 → OGD7SKFC5 → NH82SPKB6 → QJF8SJD93 → PIA5SMIA4 → OKC7SKG85 → NHC7SKGB6 → MG94SNJC7 → OGD6SLFC5 → NI92SPJA6 → QJE8SJE93 → PIA4SNIA4 → OLD7SKF75 → NHE6SLEB6 → MHA2SPIB7 → QIC6SLGA3 → PKB5SMH84 → OKE8SJE85 → NGC4SNGC6 → OHB3SOHB5 → PJD5SMF94 → OKD5SMF85 → NJE6SLE96 → MHC4SNGB7 → OGB4SNHC5 → OJC4SNG95 → OJE6SLE95 → NIC4SNGA6 → OHD5SMFB5 → NJB3SOH96 → PIE7SKEA4 → OIA3SOIA5 → PJE7SKE94 → OIB4SNHA5 → OJD6SLF95 → NIC5SMGA6 → NHC5SMGB6 → NHB4SNHB6 → OHC5SMGB5 → NJB4SNH96 → OHE7SKEB5 → NH92SPJB6 → QJE7SKE93 → PJB4SNH94 → OLE7SKE75 → NHE5SMEB6 → NHB2SPHB6 → QJC5SMG93 → PLD6SLF74 → OJE7SKE95 → NHB4SNHB6
10106 max steps400000557B → B7553ONNLI → LIIE6LEAA8 → FD87SSKKFE → LK75SSML88 → NLED0RFE76 → RHE1SSQEB2 → RQGC2PGC22 → PON43OO544 → MKKKHA8887 → FCCC6LGGGE → F4440ROOOE → RKKK0R8882 → RPCCBGGG32 → PM543OON64 → MKKIFCA887 → FCC82PKGGE → NC440ROOG6 → RKKH3OB882 → PLCC5MGG74 → LHE43OOEB8 → LKD5SSMF88 → NKE84NKE86 → JHCBSSGGBA → IH84SSNKBB → OKC90RJG85 → RJCA3OIG92 → PLA83OKI74 → MKEC7KGE87 → FDC3SSOGFE → PGB1SSQHC4 → ROFD0RFD42 → RPK21QQ832 → QOOMBG6443 → NKKG4NC886 → JHCC3OGGBA → L9643OOMJ8 → LKGD9IFC88 → DC941QOJGG → PKA42POI84 → NLKC7KG876 → HEDC3OGFEC → L541SSQON8 → ROLG1QC742 → QOKE3OE843 → NLKBSSG876 → MLFA3OID77 → LFE81QKED8 → PDC1SSQGF4 → ROEC0RGE42 → RPK3SSO832 → QPOH3OB433 → NMLK5M8766 → IGGEBGECCB → 7543SSOONM → POJH0RB944 → RLKA5MI872 → PHEC7KGEB4 → LD63SSOMF8 → PMG95MJC64 → LHGA3OICB8 → LD863OMKF8 → LGDC1QGFC8 → PD441QOOF4 → PLKK1Q8874 → PLECBGGE74 → LE53SSONE8 → PNG96LJC54 → LIFA3OIDA8 → LD881QKKF8 → PDCC1QGGF4 → PL441QOO74 → PLKKDE8874 → LECC0RGGE8 → RD43SSOOF2 → QPNB8JH533 → NMIB5MHA66 → IGG85MKCCB → HC743OOLGC → LKE53ONE88 → LIDBSSGFA8 → KIA50RNIA9 → RIB87KKHA2 → PDC85MKGF4 → LHC41QOGB8 → PKD63OMF84 → MKGC1QGC87 → PFC43OOGD4 → MKK41QO887 → PKFCBGGD84 → LC541QONG8 → PKID3OFA84 → MKC81QKG87 → PFCC3OGGD4 → MK441QOO87 → PKKFBGD884 → LCC51QNGG8 → PID43OOFA4 → MKK81QK887 → PFCCBGGGD4 → L5441QOON8 → PKKICFA884 → LCC82PKGG8 → NDC43OOGF6 → LKH41QOB88 → PKDC5MGF84 → LHC41QOGB8
11114 max stepsE000000000S → SDSSSSSSSE1 → RFDSSSSSED2 → QFFECSFEDD3 → PE220SRQQE4 → SPOMASH6431 → RPLIBSGA732 → QOIB6SLHA43 → PMIB6SLHA64 → OJGB6SLHC95 → NIC84SNKGA6 → OHFA5SMIDB5 → NJC73SOLG96 → PIGC6SLGCA4 → OJB63SOMH95 → PJID7SKFA94 → OIB94SNJHA5 → OJE96SLJE95 → NICA4SNIGA6 → OHD85SMKFB5 → NJE93SOJE96 → PIEA4SNIEA4 → OLD83SOKF75 → PJHD6SLFB94 → OJC83SOKG95 → PJGB6SLHC94 → OJC84SNKG95 → OJFB6SLHD95 → NIC83SOKGA6 → PIFA5SMIDA4 → OKC84SNKG85 → OJFC7SKGD95 → NHB72SPLHB6 → QJGA5SMIC93 → PLD95SMJF74 → OKFC5SMGD85 → NJE82SPKE96 → QJFB4SNHD93 → PME83SOKE64 → PLIE5SMEA74 → OKFB3SOHD85 → PJG93SOJC94 → PLFA6SLID74 → OJEB4SNHE95 → OJE82SPKE95 → QKGB4SNHC83 → PMF94SNJD64 → OLHD5SMFB75 → NJFA3SOID96 → PIE94SNJEA4 → OLE93SOJE75 → PJHC4SNGB94 → OLE84SNKE75 → OJGD5SMFC95 → NJD72SPLF96 → QJGC5SMGC93 → PLD73SOLF74 → PLHE7SKEB74 → OIE92SPJEA5 → QKF93SOJD83 → PNGB5SMHC54 → OKIB4SNHA85 → OJFA6SLID95 → NIC94SNJGA6 → OHE95SMJEB5 → NJD82SPKF96 → QJFB5SMHD93 → PLD83SOKF74 → PLHD6SLFB74 → OJEA3SOIE95 → PJF93SOJD94 → PLFA5SMID74 → OKFB4SNHD85 → OJF93SOJD95 → PJFA5SMID94 → OKD94SNJF85 → OJFB5SMHD95 → NJD83SOKF96 → PIFB5SMHDA4 → OKC73SOLG85 → PJHD7SKFB94 → OIB83SOKHA5 → PJGA6SLIC94 → OJC95SMJG95 → NJDA6SLIF96 → MHC94SNJGB7 → OGD84SNKFC5 → OJF82SPKD95 → QKGB5SMHC83 → PLE94SNJE74 → OLGC4SNGC75 → OJG93SOJC95 → PJFA6SLID94 → OJC94SNJG95 → OJEA6SLIE95 → NIC93SOJGA6 → PIE95SMJEA4 → OKD93SOJF85 → PJGB5SMHC94 → OKD84SNKF85 → OJFC6SLGD95 → NIC72SPLGA6 → QJGB5SMHC93 → PLD84SNKF74 → OLGD6SLFC75 → NIE92SPJEA6 → QJE93SOJE93 → PNFA4SNID54 → OLID4SNFA75 → OJGB4SNHC95 → OJE84SNKE95 → OJFB4SNHD95 → OJE83SOKE95 → PJGB4SNHC94 → OLE84SNKE75
1271 max steps40000004677B → B77643OOMLLI → LKGEE6LEEC88 → FDC3SSSSOGFE → PGFE90RJEDC4 → RLA41SSQOI72 → RQNJE2PE9522 → PONI9SSIA544 → OOKFCSSFD845 → ONGC6SSLGC55 → NNIB8SSJHA56 → NMFD80RKFD66 → RHGC21QQGCB2 → QOO643OOM443 → NLKKKFC88876 → HECCC2PGGGEC → N5443SSOOON6 → POKJHSSA9844 → OOHFA1QIDB45 → PKJ861QMK984 → PLGCC9IGGC74 → LE9443OOOJE8 → LKKD9SSIF888 → KKDB72PLHF89 → NECB61QMHGE6 → PHG63SSOMCB4 → POJDA0RIF944 → RLKA81QKI872 → QOECC7KGGE43 → NKD43SSOOF86 → POIGA4NICA44 → LKJ883OKK988 → LDCCC9IGGGF8 → D94441QOOOJG → PKKKA2PI8884 → NLCCC7KGGG76 → HED443OOOFEC → LKK51SSQN888 → RNIFCSSFDA52 → QNHB4SSNHB53 → POLCBSSGG744 → OOID8SSJFA45 → ONGE62PMEC55 → NJIG3SSOCA96 → PMFD71QLFD64 → PLGE21QQEC74 → POLE3SSOE744 → POLHA6LIB744 → LKFE85MKED88 → HDCC1SSQGGFC → RGE530RPNEC2 → RPMI3SSOA632 → QPOJE3OE9433 → NMLK9SSI8766 → MMGEC1QGEC67 → PGF43SSOODC4 → POLCB0RHG744 → RLKE63OME872 → PLGEBSSGEC74 → OLE921QQJE75 → POJE9SSIE944 → OOGF53ONDC45 → LKJI41QOA988 → PKDCA7KIGF84 → LDC841QOKGF8 → PKDC41QOGF84 → PLKC41QOG874 → PLKEC3OGE874 → MKEC3SSOGE87 → PLGA61QMIC74 → PLGE83OKEC74 → MKEC3SSOGE87