Base 30: Cycles Sequences: All Cycle Counts

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 # Full Cycles
(excluding zero)		 Frequency Cycle
Length		 Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
23 cycles145×(max) 5 nodes⮎ 0T → S1 → Q3 → M7 → EF ⮌
145×(max) 5 nodes⮎ 2R → O5 → IB → 6N → GD ⮌
145×(max) 5 nodes⮎ 4P → K9 → AJ → 8L → CH ⮌
31 cycle 4,930×(fixed) (max) 1 node ⮎ ETF ⮌
47 cycles9,860×(max) 4 nodes⮎ 61RO → QHB4 → M5N8 → IDFC ⮌
7,817×(max) 4 nodes⮎ E1RG → Q1R4 → QL74 → MDF8 ⮌
7,347×(max) 4 nodes⮎ E5NG → I1RC → Q5N4 → MHB8 ⮌
7,249×(max) 4 nodes⮎ A1RK → Q9J4 → M9J8 → E9JG ⮌
4,323×2 nodes⮎ A5NK → I9JC ⮌
2,872×2 nodes⮎ M1R8 → QDF4 ⮌
1,422×(fixed) 1 node ⮎ I5NC ⮌
52 cycles277,298×(fixed) 1 node ⮎ K9TJA ⮌
928×(max) 2 nodes⮎ FDTFF → FTTTE ⮌
68 cycles1,227,205×(max) 47 nodes⮎ 750SON → SJFDA2 → Q91RK4 → QMAI74 → MF7LE8 → FD0SGF → S2TTQ2 → RR1R23 → QPN544 → MLHB88 → ED5NGG → I31RQC → QN5N64 → MIGCB8 → E73PMG → MF1RE8 → QE0SF4 → SM0S72 → SQEE32 → QMTT64 → PN3P65 → MKGC98 → EB3PIG → M71RM8 → QFDFE4 → M20SR8 → SPDF42 → QL1R84 → QMCG74 → MF3PE8 → ME0SF8 → SE0SF2 → SQ0S32 → SQM632 → QNFD64 → MH1RC8 → QE4OF4 → MK0S98 → SEAIF2 → Q80SL4 → SMCG72 → QF3PE4 → NL0S87 → SGCGD2 → Q42QP4 → OMK876 → IFBHEC ⮌
197,596×15 nodes⮎ 640SPO → SLHB82 → QD5NG4 → MI2QB8 → OE6MF6 → IG0SDC → S62QN2 → QOGC54 → MJ3PA8 → ME8KF8 → EC0SHG → S51RO2 → RPIA43 → OL7L86 → IECGFC ⮌
118,403×5 nodes⮎ KE2QFA → OA0SJ6 → SI8KB2 → QC6MH4 → MG4OD8 ⮌
38,269×5 nodes⮎ KI0SBA → SA6MJ2 → QG8KD4 → MC2QH8 → OE4OF6 ⮌
19,109×7 nodes⮎ HF3PED → M40SP8 → SLDF82 → QD1RG4 → QM2Q74 → OMEE76 → IETTEC ⮌
11,362×5 nodes⮎ KA0SJA → SA8KJ2 → QC8KH4 → MC4OH8 → KE4OFA ⮌
10,946×5 nodes⮎ MG2QD8 → OE2QF6 → OI0SB6 → SI6MB2 → QG6MD4 ⮌
240×(fixed) 1 node ⮎ FETTEF ⮌
71 cycle 8,347,650×(max) 4 nodes⮎ ME5TNF8 → OF7TLE6 → NH6TMC7 → NG9TJD7 ⮌
84 cycles27,048,382×(max) 10 nodes⮎ MKB0SI98 → SEB6MIF2 → QG70SMD4 → SMF2QE72 → QOF0SE54 → SMJ0SA72 → SQF8KE32 → QNC0SH64 → SMH4OC72 → QKF4OE94 ⮌
11,513,935×(max) 10 nodes⮎ MKJ0SA98 → SEB8KIF2 → QC70SMH4 → SMF4OE72 → QKF0SE94 → SMB0SI72 → SQF6ME32 → QNG0SD64 → SMH2QC72 → QOF4OE54 ⮌
37,399×3 nodes⮎ IG94OKDC → KB62QNIA → OHA6MJC6 ⮌
8,274×(fixed) 1 node ⮎ KJ9TTJAA ⮌
93 cycles142,659,246×(fixed) 1 node ⮎ OIC5TNHB6 ⮌
20,352,124×(max) 6 nodes⮎ NID5TNGB7 → OGC4TOHD6 → PIC3TPHB5 → QKE5TNF94 → PLE5TNF85 → OKF6TME96 ⮌
240×(fixed) 1 node ⮎ FFETTTEEF ⮌
105 cycles548,574,350×(max) 90 nodes⮎ MKB10SSI98 → SREB6MIF22 → QPG70SMD44 → SMLF2QE872 → QOFD0SGE54 → SMJ30SQA72 → SQNF8KE632 → QNHC0SHC64 → SMH54OOC72 → QKJF4OEA94 → MKB90SKI98 → SEBB6MIIF2 → QG770SMMD4 → SMFF2QEE72 → QOF10SSE54 → SRMJ0SA722 → SQPF8KE432 → QNLC0SH864 → SMHD4OGC72 → QKF52QOE94 → OMJB0SIA76 → SIF96MKEB2 → QGB70SMID4 → SMF72QME72 → QOFF0SEE54 → SMJ10SSA72 → SRQF8KE322 → QPNC0SH644 → SMLH4OC872 → QKFD4OGE94 → MKB30SQI98 → SNEB6MIF62 → QHG70SMDC4 → SMF52QOE72 → QOJF0SEA54 → SMJ90SKA72 → SQFB8KIE32 → QNC70SMH64 → SMHF4OEC72 → QKF50SOE94 → SMJB0SIA72 → SQF96MKE32 → QNGB0SID64 → SMH72QMC72 → QOFF4OEE54 → MKJ10SSA98 → SREB8KIF22 → QPC70SMH44 → SMLF4OE872 → QKFD0SGE94 → SMB30SQI72 → SQNF6ME632 → QNHG0SDC64 → SMH52QOC72 → QOJF4OEA54 → MKJ90SKA98 → SEBB8KIIF2 → QC770SMMH4 → SMFF4OEE72 → QKF10SSE94 → SRMB0SI722 → SQPF6ME432 → QNLG0SD864 → SMHD2QGC72 → QOF52QOE54 → OMJJ0SAA76 → SIF98KKEB2 → QCB70SMIH4 → SMF74OME72 → QKFF0SEE94 → SMB10SSI72 → SRQF6ME322 → QPNG0SD644 → SMLH2QC872 → QOFD4OGE54 → MKJ30SQA98 → SNEB8KIF62 → QHC70SMHC4 → SMF54OOE72 → QKJF0SEA94 → SMB90SKI72 → SQFB6MIE32 → QNG70SMD64 → SMHF2QEC72 → QOF50SOE54 → SMJJ0SAA72 → SQF98KKE32 → QNCB0SIH64 → SMH74OMC72 → QKFF4OEE94 ⮌
82,380,423×12 nodes⮎ KI970SMKBA → SFBA6MJIE2 → QG970SMKD4 → SMFB2QIE72 → QOF70SME54 → SMJF0SEA72 → SQF90SKE32 → SQNB0SI632 → SQNH6MC632 → QNHG4ODC64 → MKH52QOC98 → OJEB4OIFA6 ⮌
2,953,242×3 nodes⮎ QNKF0SE964 → SMHB0SIC72 → SQF74OME32 ⮌
1,832,521×12 nodes⮎ ECB90SKIHG → SB751ROMI2 → RPJF6MEA43 → OLG90SKD86 → SIDB2QIGB2 → QO772QMM54 → OMJFEEEA76 → IF90TTSKEC → TKG62QND91 → SOHB2QIC52 → QOJ74OMA54 → MKJF8KEA98 ⮌
4,830×(fixed) 1 node ⮎ KKA9TTJJ9A ⮌
114 cycles2,267,713,758×(max) 25 nodes⮎ OIEA4TOJFB6 → PIE83TPLFB5 → QKHA3TPJC94 → QMGA6TMJD74 → PKFC5TNHE95 → OKE82TQLF96 → RKGC5TNHD93 → QME83TPLF74 → QMIE6TMFB74 → PKFB3TPIE95 → QKG93TPKD94 → QMGB6TMID74 → PKFB4TOIE95 → PKF93TPKE95 → QKGB5TNID94 → PLE94TOKF85 → PKGC5TNHD95 → OKE83TPLF96 → QJGC5TNHDA4 → PLD73TPMG85 → QKIE7TLFB94 → PJC93TPKHA5 → QKGA6TMJD94 → PKDA5TNJG95 → OKEA5TNJF96 ⮌
37,390,404×(fixed) 1 node ⮎ PKFA4TOJE95 ⮌
6,691,418×4 nodes⮎ OIA64TONJB6 → PIID7TLGBB5 → OIA74TOMJB6 → PIHC7TLHCB5 ⮌
5,830×(fixed) 1 node ⮎ KJJ9TTTJAAA ⮌
126 cycles5,375,528,625×(max) 70 nodes⮎ MKB910SSKI98 → SREBB6MIIF22 → QPG770SMMD44 → SMLFF2QEE872 → QOFD10SSGE54 → SRMJ30SQA722 → SQPNF8KE6432 → QNLHC0SHC864 → SMHD54OOGC72 → QKJF52QOEA94 → OMJB90SKIA76 → SIFB96MKIEB2 → QGB770SMMID4 → SMFF72QMEE72 → QOFF10SSEE54 → SRMJ10SSA722 → SRQPF8KE4322 → QPNLC0SH8644 → SMLHD4OGC872 → QKFD52QOGE94 → OMJB30SQIA76 → SNIF96MKEB62 → QHGB70SMIDC4 → SMF752QOME72 → QOJFF0SEEA54 → SMJ910SSKA72 → SRQFB8KIE322 → QPNC70SMH644 → SMLHF4OEC872 → QKFD50SOGE94 → SMJB30SQIA72 → SQNF96MKE632 → QNHGB0SIDC64 → SMH752QOMC72 → QOJFF4OEEA54 → MKJ910SSKA98 → SREBB8KIIF22 → QPC770SMMH44 → SMLFF4OEE872 → QKFD10SSGE94 → SRMB30SQI722 → SQPNF6ME6432 → QNLHG0SDC864 → SMHD52QOGC72 → QOJF52QOEA54 → OMJJ90SKAA76 → SIFB98KKIEB2 → QCB770SMMIH4 → SMFF74OMEE72 → QKFF10SSEE94 → SRMB10SSI722 → SRQPF6ME4322 → QPNLG0SD8644 → SMLHD2QGC872 → QOFD52QOGE54 → OMJJ30SQAA76 → SNIF98KKEB62 → QHCB70SMIHC4 → SMF754OOME72 → QKJFF0SEEA94 → SMB910SSKI72 → SRQFB6MIE322 → QPNG70SMD644 → SMLHF2QEC872 → QOFD50SOGE54 → SMJJ30SQAA72 → SQNF98KKE632 → QNHCB0SIHC64 → SMH754OOMC72 → QKJFF4OEEA94 ⮌
1,424,641,780×20 nodes⮎ MKB310SSQI98 → SRNEB6MIF622 → QPHG70SMDC44 → SMLF52QOE872 → QOJFD0SGEA54 → SMJ930SQKA72 → SQNFB8KIE632 → QNHC70SMHC64 → SMHF54OOEC72 → QKJF50SOEA94 → SMJB90SKIA72 → SQFB96MKIE32 → QNGB70SMID64 → SMHF72QMEC72 → QOFF50SOEE54 → SMJJ10SSAA72 → SRQF98KKE322 → QPNCB0SIH644 → SMLH74OMC872 → QKFFD4OGEE94 ⮌
870,474,232×20 nodes⮎ MKJ310SSQA98 → SRNEB8KIF622 → QPHC70SMHC44 → SMLF54OOE872 → QKJFD0SGEA94 → SMB930SQKI72 → SQNFB6MIE632 → QNHG70SMDC64 → SMHF52QOEC72 → QOJF50SOEA54 → SMJJ90SKAA72 → SQFB98KKIE32 → QNCB70SMIH64 → SMHF74OMEC72 → QKFF50SOEE94 → SMJB10SSIA72 → SRQF96MKE322 → QPNGB0SID644 → SMLH72QMC872 → QOFFD4OGEE54 ⮌
213,868,082×25 nodes⮎ MKB930SQKI98 → SNEBB6MIIF62 → QHG770SMMDC4 → SMFF52QOEE72 → QOJF10SSEA54 → SRMJ90SKA722 → SQPFB8KIE432 → QNLC70SMH864 → SMHFD4OGEC72 → QKF530SQOE94 → SNMJB0SIA762 → SQHF96MKEC32 → QNGB50SOID64 → SMJH72QMCA72 → QOFF94OKEE54 → MKJB10SSIA98 → SREB96MKIF22 → QPGB70SMID44 → SMLF72QME872 → QOFFD0SGEE54 → SMJ310SSQA72 → SRQNF8KE6322 → QPNHC0SHC644 → SMLH54OOC872 → QKJFD4OGEA94 ⮌
14,141,931×6 nodes⮎ KE7530SQOMFA → SNJFA0SJEA62 → SQH990SKKC32 → SQNBB4OII632 → QNKH76MMC964 → MHGFB4OIEDC8 ⮌
240×(fixed) 1 node ⮎ FFFETTTTEEEF ⮌
13+---Not showing digit sets 13+ due to verbosity.