Base 38: Cycles Sequences: All Cycle Counts

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 # Full Cycles
(excluding zero)		 Frequency Cycle
Length		 Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
23 cycles444×(max) 12 nodes⮎ 0b → a1 → Y3 → U7 → MF → 6V → OD → AR → GL → 4X → S9 → IJ ⮌
222×6 nodes⮎ 2Z → W5 → QB → EN → 8T → KH ⮌
37×(fixed) 1 node ⮎ CP ⮌
31 cycle 9,842×(fixed) (max) 1 node ⮎ IbJ ⮌
44 cycles25,601×(max) 9 nodes⮎ A1ZS → YHJ4 → U1Z8 → YLF4 → U5V8 → QLFC → E5VO → Q9RC → IDNK ⮌
25,592×(max) 9 nodes⮎ E9RO → I9RK → I1ZK → Y1Z4 → YT74 → ULF8 → M5VG → Q5VC → QDNC ⮌
25,407×(max) 9 nodes⮎ 61ZW → YPB4 → UDN8 → M9RG → I5VK → Q1ZC → YDN4 → U9R8 → MHJG ⮌
24,632×(max) 9 nodes⮎ A5VS → QHJC → E1ZO → Y9R4 → UHJ8 → M1ZG → Y5V4 → UPB8 → MDNG ⮌
52 cycles849,150×(max) 4 nodes⮎ PBbPD → QBbPC → QDbNC → PCbOD ⮌
1,480×2 nodes⮎ JHbJJ → JbbbI ⮌
66 cycles4,391,163×(max) 57 nodes⮎ C60aVQ → aPDNC2 → YD9RO4 → UIAQJ8 → MG0aLG → a64WV2 → YSOC94 → UJBPI8 → ME0aNG → a95VS2 → YQIIB4 → UEbbM8 → TN7TE9 → MK8SHG → K62YVI → WP1ZC6 → YQCOB4 → UFBPM8 → ME6UNG → O95VSE → QJ9RIC → IE0aNK → a91ZS2 → ZXII43 → WSbb86 → VT3X87 → UOKGD8 → MB3XQG → UF5VM8 → QM6UFC → OE6UNE → OA8SRE → KH9RKI → I31ZYK → YV1Z64 → YUOC74 → UNBPE8 → ME8SNG → K95VSI → QJ1ZIC → YE0aN4 → aU8S72 → YNJHE4 → U91ZS8 → YMIIF4 → U6bbU8 → VSbb87 → UT2Y88 → WMKGF6 → Q73XUC → UNDNE8 → MA8SRG → KH5VKI → Q31ZYC → YVDN64 → UP9RC8 → MICOJG ⮌
1,179,210×6 nodes⮎ MK4WHG → S62YVA → WPHJC6 → QD1ZOC → YEAQN4 → UG8SL8 ⮌
410,078×11 nodes⮎ FD6UON → OB7TQE → MF9RMG → I75VUK → QN1ZEC → YE8SN4 → UK8SH8 → MK2YHG → W62YV6 → WQOCB6 → QFBPMC ⮌
77,206×2 nodes⮎ QA2YRC → WHDNK6 ⮌
38,379×6 nodes⮎ QO0aDC → aEAQN2 → YG8SL4 → UK4WH8 → SM2YFA → WI6UJ6 ⮌
380×(fixed) 1 node ⮎ JIbbIJ ⮌
71 cycle 38,320,530×(max) 4 nodes⮎ SI7bTJA → UJ9bRI8 → TL8bSG9 → TKBbPH9 ⮌
84 cycles109,863,948×(max) 93 nodes⮎ CA30aYRQ → aVHDNK62 → YPA2YRC4 → WUHCOK76 → QNC2YPEC → WED8SON6 → QKB8SQHC → KFE2YNMI → W971ZUS6 → YQNIIEB4 → UF8bbSM8 → TTF5VM89 → QLK6UHGC → OE52YWNE → WRA8SRA6 → QKHGKKHC → E432YYXO → WVT9R866 → QPLHJGCC → ED51ZWOO → YRB9RQA4 → UIHEMKJ8 → M830aYTG → aVL5VG62 → YQP4WCB4 → USFCOM98 → MJC6UPIG → OD60aVOE → aPB9RQC2 → YIFCOMJ4 → UC70aUP8 → aNMCOFE2 → YC96USP4 → UOJCOID8 → MCB0aQPG → aFD5VOM2 → YQB6UQB4 → UOFEMMD8 → MB86UTQG → OLF5VMGE → QA74WURC → SNHDNKEA → IA92YSRK → WJH1ZKI6 → YQ30aYB4 → aVUEM762 → YPN7TEC4 → UMD8SOF8 → MKB6UQHG → OF62YVME → WPA6URC6 → QOHCOKDC → ECB2YQPO → WFD9ROM6 → QIB6UQJC → OFE0aNME → aA96USR2 → YOJGKID4 → UB40aXQ8 → aTMEMF82 → YL86UTG4 → UOL4WGD8 → SMB4WQFA → SIF6UMJA → OI70aUJE → aNA0aRE2 → aYH8SK32 → YVK2YH64 → WUP2YC76 → WQNCOEB6 → QFC8SPMC → KED6UONI → OB91ZSQE → YJF9RMI4 → UI70aUJ8 → aNM0aFE2 → aY96US32 → YVOIID64 → UPAbbQC8 → TRI0aJA9 → aKH0aKH2 → aY32YY32 → YWVU6654 → URPNDCA8 → MHD9ROKG → IB62YVQK → WPF1ZMC6 → YQD6UOB4 → UOFAQMD8 → MGB6UQLG → OF64WVME → SPA6URCA → OIHCOKJE ⮌
56,542,937×53 nodes⮎ A410aaXS → aZTHJ822 → YXL1ZG44 → YUT4W874 → USNKGE98 → MJ93XSIG → UJ60aVI8 → aPM0aFC2 → aYD6UO32 → YVOAQD64 → UPGAQLC8 → MGD4WOLG → SB64WVQA → SPIEMJCA → ID80aTOK → aLB1ZQG2 → ZXF4WM43 → WTS6U986 → QOLIIGDC → EB4bbWQO → XQI1ZJB5 → YSF0aM94 → aUJ6UI72 → YON0aED4 → aUB8SQ72 → YNKEMHE4 → U982YTS8 → WMLIIGF6 → Q74bbWUC → XUK3XH75 → USN2YE98 → WMJ8SIF6 → QK70aUHC → aNE2YNE2 → YW98SS54 → URKIIHA8 → MH2bbYKG → ZLH1ZKG3 → YW52YW54 → WURQAA76 → QNHFLKEC → E962YVSO → WPJ9RIC6 → QID0aOJC → aEB0aQN2 → aYF8SM32 → YVK6UH64 → UPO2YDC8 → WMDAQOF6 → QGB6UQLC → OFE4WNME → SA96USRA → OJIGKJIE ⮌
43,518,611×47 nodes⮎ C720aZUQ → aXNDNE42 → YTA8SR84 → ULKGKHG8 → M542YXWG → WTR5VA86 → RPLGKGCB → GD53XWOM → URB5VQA8 → QMHEMKFC → E872YUTO → WNL9RGE6 → QI94WSJC → SJE0aNIA → aI90aSJ2 → aYJ0aI32 → aYV0a632 → aYVOC632 → YVPBPC64 → UPECONC8 → MDC8SPOG → KDB5VQOI → QFB1ZQMC → YFE6UNM4 → UO96USD8 → OMJAQIFE → GA70aURM → aNH5VKE2 → YQ92YSB4 → WUJEMI76 → QN80aTEC → aLE8SNG2 → YK94WSH4 → USJ2YI98 → WMJ0aIF6 → aQ70aUB2 → aYNEME32 → YV97TS64 → UPMIIFC8 → MD6bbUOG → VOE1ZND7 → YOB8SQD4 → UKFAQMH8 → MG72YULG → WN64WVE6 → SQP8SCBA → KIFCOMJI ⮌
5,627,661×12 nodes⮎ IFE6UNMK → O971ZUSE → YNJ9RIE4 → UI90aSJ8 → aMJ0aIF2 → aY70aU32 → aYVME632 → YVP7TC64 → UPMCOFC8 → MDC6UPOG → ODB5VQOE → QFB9RQMC ⮌
95 cycles529,989,858×(max) 10 nodes⮎ UNF6bUME8 → VMG7bTLF7 → UOE5bVND8 → WNH9bRKE6 → VND5bVOE7 → WOI9bRJD6 → VNE5bVNE7 → WOH8bSKD6 → VOF6bUMD7 → VOH8bSKD7 ⮌
383,406,160×2 nodes⮎ VOF5bVMD7 → WOI8bSJD6 ⮌
186,754,312×4 nodes⮎ UME5bVNF8 → WNG7bTLE6 → VPF6bUMC7 → VOI9bRJD7 ⮌
1,565,582×(fixed) 1 node ⮎ VOH6bUKD7 ⮌
380×(fixed) 1 node ⮎ JJIbbbIIJ ⮌
102 cycles3,558,279,362×77 nodes⮎ KIFD0aOMJI → aB720aZUQ2 → aYXNEME432 → YVT97TS864 → UPMLIIGFC8 → MD74bbWUOG → XUJE1ZNI75 → YSN90aSE94 → aUJJ8SII72 → YNK10aaHE4 → aZU92YS722 → YXWNIIE544 → UTR8bbSA88 → TTMJ0aIF89 → aLK70aUHG2 → aYN52YWE32 → YWVR8SA654 → URPKGKHCA8 → MHD42YXOKG → WTB62YVQ86 → WQPLEMGCB6 → QFD84WTOMC → SLEB6UQNGA → OIF94WSMJE → SJA70aURIA → aNIH0aKJE2 → aY930aYS32 → aYVVII6632 → YVPObbCC64 → XVMJ0aIF65 → aSP70aUC92 → aYNJCOIE32 → YVC90aSP64 → aUPJCOIC72 → YNDC0aPOE4 → aUDB8SQO72 → YNKFAQMHE4 → UG972YUSL8 → WNMJ4WIFE6 → SQ970aUSBA → aNJIEMJIE2 → Y9810aaTS4 → aZULIIG722 → YXN4bbWE44 → XXUJ8SI745 → TSNK0aHE99 → aKJ92YSIH2 → YWJ30aYI54 → aVUR0aA762 → aYPNGKEC32 → YVD93XSO64 → VTPJAQIC87 → OLGD0aOLGE → aBA54WWRQ2 → YSRHEMKA94 → UJH82YTKI8 → WML30aYGF6 → aVQ74WUB62 → YSPNEMEC94 → UJD97TSOI8 → NLJB0aQIGF → aF850aWTM2 → aYRL6UGA32 → YVOH4WKD64 → USPB2YQC98 → WMJFCOMIF6 → QC770aUUPC → aNNECONEE2 → YC998SSSP4 → UKJJCOIIH8 → MC310aaYPG → aZVD5VO622 → YXQPAQCB44 → UTGFCOML88 → MLC74WUPGG → SND64WVOEA → SPIB8SQJCA ⮌
1,619,787,351×(max) 118 nodes⮎ GB874WUTQM → SNLF5VMGEA → QI974WUSJC → SNJE0aNIEA → aI990aSSJ2 → aYJJ0aII32 → aYV10aa632 → aZYVOC6322 → YXVPBPC644 → UTPECONC88 → MLDC8SPOGG → KDB64WVQOI → SPFB1ZQMCA → YIFD6UOMJ4 → UOB70aUQD8 → aNMFAQMFE2 → YG976UUSL4 → UONJ4WIED8 → SMB90aSQFA → aJIF6UMJI2 → YO710aaUD4 → aZUNAQE722 → YXNG8SLE44 → UTK94WSH88 → SMLJ2YIGFA → WI750aWUJ6 → aRQN0aEBA2 → aYHF8SMK32 → YVK72YUH64 → WUPN2YEC76 → WQND8SOEB6 → QKFB8SQMHC → KFE72YUNMI → WN971ZUSE6 → YQNJ8SIEB4 → UKF90aSMH8 → aMJ72YUIF2 → YWN70aUE54 → aURN8SEA72 → YNKH8SKHE4 → UK932YYSH8 → WVMJ2YIF66 → WQP70aUCB6 → aQNFCOMEB2 → YFC96USPM4 → UOJD6UOID8 → OMBB0aQQFE → aFFA6URMM2 → YOH76UUKD4 → UONB2YQED8 → WMFB8SQMF6 → QKF76UUMHC → ONE72YUNEE → WNA98SSRE6 → QKJH8SKIHC → KE330aYYNI → aVV91ZS662 → ZXPPIICC43 → WTDCbbOO86 → VTKFbbLH87 → UTGC0aPL88 → aMLD4WOGF2 → YSB74WUQ94 → USNJEMIE98 → MJ980aTSIG → aLJ60aVIG2 → aYP50aWC32 → aYVRCOA632 → YVPHBPKC64 → UPED2YONC8 → WMDB8SQOF6 → QKFB6UQMHC → OFE72YUNME → WNA96USRE6 → QOJH8SKIDC → KEB30aYQNI → aVF91ZSM62 → ZXPJ6UIC43 → WTOD0aOD86 → aQLBAQQGB2 → YGFF4WMML4 → US774WUU98 → SNNMIIFEEA → I996bbUSSK → VSLA7TRG97 → OMJH4WKIFE → SA730aYURA → aVNIGKJE62 → YP940aXSC4 → aUTJCOI872 → YNLC0aPGE4 → aUD94WSO72 → YSNJAQIE94 → UJG90aSLI8 → aMJ50aWIF2 → aYR70aUA32 → aYVNGKE632 → YVP93XSC64 → VTPJCOIC87 → OLDC0aPOGE → aDBA4WRQO2 → YSHFAQMK94 → UJG72YULI8 → WNM50aWFE6 → aRQ96USBA2 → YOJHEMKID4 → UB830aYTQ8 → aVMLEMGF62 → YP874WUTC4 → USNLCOGE98 → MJC94WSPIG → SJD60aVOIA → aPIB0aQJC2 → aYFD0aOM32 → aYVB6UQ632 → YVPOEMDC64 → UPDB7TQOC8 → NLFDAQOMGF ⮌
11+---Not showing digit sets 11+ due to verbosity.