Base 29: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
23 max steps10 → 0S → R1 → P3
315 max steps100 → 0SS → RS1 → QS2 → PS3 → OS4 → NS5 → MS6 → LS7 → KS8 → JS9 → ISA → HSB → GSC → FSD → ESE
44 max stepsF000 → ESSE → EDEF → 1SSR → R0R2
515 max steps30000 → 2SSSQ → Q1SQ3 → RMS52 → QLS63 → PJS84 → OGSB5 → NCSF6 → MASH7 → LBSG8 → K9SI9 → JASHA → I8SJB → K7SK9 → LASH8 → KASH9
649 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
727 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
861 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
945 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
1084 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
1152 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
1268 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