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 steps100
27 max steps10 → 0S → R1 → P3L7DF1RP3
317 max steps100 → 0SS → RS1 → QS2 → PS3 → OS4 → NS5 → MS6 → LS7 → KS8 → JS9 → ISA → HSB → GSC → FSD → ESEDSFESE
418 max stepsF000 → ESSE → EDEF → 1SSR → R0R2RO32PK74LCF8D2PGN2P6NGB6H4NCJ4NAJ8JAB8JIB6LIF6LEF0RER0R2
519 max steps30000 → 2SSSQ → Q1SQ3 → RMS52 → QLS63 → PJS84 → OGSB5 → NCSF6 → MASH7 → LBSG8 → K9SI9 → JASHA → I8SJB → K7SK9 → LASH8 → KASH9J9SIAJ8SJAK8SJ9KASH9
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 → H51QNCPI4NA4LJ7K98EC9IGF940ROKRKAH82PC6LG4LF3OD8LD1QF8PD1QF4PL1Q74PLDE74LE0RE8RCSSF2QGBGC3N53ON6LIGBA8D84NKGJC2PGAN93OJ6LH9IB8D95MJGHA2PICN84NK6JHBGBA964NMKJGAHCA973OLKLEAHE8D6SSLGMF4ND7JF1QDAP91QJ4PL9I74LE8JE8DASSHGIF0RDBR71QL2QODE43NK0R86RHBGB2P64NM4LJFC98DA2PIGN82PK6NHBGB6H64NMCJG4NCAJ93OJALA8JI8DB7KHGD62PMGNG2PC6NH3OB6LH5MB8HD5MFCH51QNC
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 → LF6SLD8MD7SKF7LF6SLD8
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 → MK81QK87PFCBGGD4L541QON8PKICFA84LC82PKG8NDC3OGF6LH41QOB8PKD5MF84LHC1QGB8PD63OMF4MKG1QC87PFC3OGD4MK41QO87PKFBGD84LC51QNG8PID3OFA4MK81QK87
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 → NHB4SNHB6OHC5SMGB5NJB4SNH96OHE7SKEB5NH92SPJB6QJE7SKE93PJB4SNH94OLE7SKE75NHE5SMEB6NHB2SPHB6QJC5SMG93PLD6SLF74OJE7SKE95NHB4SNHB6
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 → LHC41QOGB8PKD63OMF84MKGC1QGC87PFC43OOGD4MKK41QO887PKFCBGGD84LC541QONG8PKID3OFA84MKC81QKG87PFCC3OGGD4MK441QOO87PKKFBGD884LCC51QNGG8PID43OOFA4MKK81QK887PFCCBGGGD4L5441QOON8PKKICFA884LCC82PKGG8NDC43OOGF6LKH41QOB88PKDC5MGF84LHC41QOGB8
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 →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
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 → MKEC3SSOGE87PLGA61QMIC74PLGE83OKEC74MKEC3SSOGE87