Base 40: 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---
22 cycles390×(max) 10 nodes⮎ 0d → c1 → a3 → W7 → OF → 8V → MH → 4Z → U9 → KJ ⮌
390×(max) 10 nodes⮎ 2b → Y5 → SB → GN → 6X → QD → CR → EP → AT → IL ⮌
31 cycle 11,440×(fixed) (max) 1 node ⮎ JdK ⮌
41 cycle 123,370×(fixed) (max) 1 node ⮎ O7VG ⮌
53 cycles721,176×3 nodes⮎ QBdRE → SCdQC → RFdND ⮌
363,154×(max) 4 nodes⮎ QCdQE → RBdRD → SDdPC → REdOD ⮌
1,638×2 nodes⮎ KIdKK → KdddJ ⮌
65 cycles7,767,950×(max) 33 nodes⮎ E86WVQ → QNBRGE → GC6WRO → QF7VOE → OC8URG → MF7VOI → O93ZUG → WL7VI8 → PN2aGF → YA6WT6 → SQIKDC → GD1bQO → aD7VQ4 → WOCQF8 → OE8UPG → MB7VSI → OH3ZMG → W84YV8 → UOMGFA → K95XUK → SKddIC → RL7VID → OE2aPG → YB7VS6 → SOGMFC → G95XUO → SL7VIC → OG2aNG → Y86WV6 → SQMGDC → GD5XQO → SD7VQC → OGCQNG ⮌
331,220×2 nodes⮎ C86WVS → QNFNGE ⮌
30,442×2 nodes⮎ W91bU8 → aOKIF4 ⮌
14,988×(fixed) 1 node ⮎ OD7VQG ⮌
420×(fixed) 1 node ⮎ KJddJK ⮌
72 cycles45,482,002×(max) 19 nodes⮎ TI8dULB → VJAdSK9 → UL8dUIA → VKBdRJ9 → UK7dVJA → WLAdSI8 → VM9dTH9 → UMBdRHA → TJ9dTKB → UI9dTLA → UKAdSJA → TK8dUJB → VJ9dTK9 → UM9dTHA → UKBdRJA → TJ7dVKB → WK9dTJ8 → VN9dTG9 → UMCdQHA ⮌
8,042,638×(fixed) 1 node ⮎ UK9dTJA ⮌
84 cycles181,021,213×(max) 117 nodes⮎ E940cZUQ → cVLBRI82 → aNG2aNG4 → YW76WW76 → SQPOEEDC → GDB9TSQO → KHD7VQMK → OD4ddYQG → ZQI1bLD5 → aUD2aQ94 → YWLCQI76 → SPE2aPEC → YGBASSN6 → SIH6WMLC → QG52aYNE → YTC6WRA6 → SQJEOKDC → GDA0cTQO → cJD7VQK2 → aOD0cQF4 → cWD8UQ72 → aPMCQHE4 → WEB4YSP8 → UOHASMFA → KI94YULK → UL2ddaIA → bTI8ULA3 → YMJ2aKH6 → YS50cYB6 → cTSGMBA2 → aJH5XMK4 → WS50cYB8 → cTOGMFA2 → aJ95XUK4 → WSL0cIB8 → cOH2aMF2 → aY94YU54 → WUTKIA98 → OLJ1bKIG → a830caV4 → cXWMG762 → aRP5XEC4 → WSFASOB8 → OIH8UMLG → M852aYVI → YTN3ZGA6 → WSJ6WKB8 → QOH0cMFE → cC94YUR2 → aULEOI94 → WLA2aTI8 → YOJ2aKF6 → YS90cUB6 → cSLGMIB2 → aH62aXM4 → YWR4YC76 → USPEOEBA → KHB9TSMK → KH4ddYMK → ZME1bPH5 → aUB4YS94 → WULGMI98 → OL62aXIG → YR82aVC6 → YSNEOGB6 → SHA6WTMC → QJG4YNKE → UC70cWRA → cPKEOJE2 → aBA0cTS4 → cWJGMK72 → aP60cXE4 → cWRASC72 → aPIEOLE4 → WBA2aTS8 → YOJGMKF6 → S960cXUC → cRLFNIC2 → aF82aVO4 → YWN8UG76 → SPM6WHEC → QGB4YSNE → UHC6WRMA → QKF4YOJE → UC90cURA → cLKEOJI2 → aA30caT4 → cXWIK762 → aRP1bEC4 → aWFASO74 → WPI8ULE8 → OMB2aSHG → YH84YVM6 → USN4YGBA → UKH6WMJA → QK50cYJE → cTC0cRA2 → caJEOK32 → aXA0cT64 → cWRIKC72 → aPF1bOE4 → aWB8US74 → WPMGMHE8 → OB64YXSG → URH7VMCA → OKF4YOJG → U980cVUA → cNLJJIG2 → a72ddaW4 → bZT3ZA43 → YWVIK876 → SPN1bGEC → aGB6WSN4 → WQH6WMD8 → QOD4YQFE → UDC8URQA → MKFCQOJI ⮌
111,470,523×15 nodes⮎ 6540cZYY → cVTRBA82 → aNJFNKG4 → W870cWV8 → cPOMGFE2 → aB95XUS4 → WSLGMIB8 → OH62aXMG → YR84YVC6 → USNEOGBA → KHA6WTMK → QJ4ddYKE → ZPF5XOE5 → USB8USBA → MKHGMMJI ⮌
21,948,183×25 nodes⮎ KB91bUSK → aLGddMI4 → ZNI0cLG5 → cU72aW92 → aYPKIE54 → WTB1bSA8 → aOJGMKF4 → W960cXU8 → cROKIFC2 → aF91bUO4 → aWL8UI74 → WPM2aHE8 → YOB4YSF6 → USH8UMBA → MKH4YMJI → U540cZYA → cVTJJA82 → aNIddKG4 → ZNI2aLG5 → YU72aW96 → YSPKIEB6 → SHB1bSMC → aHG4YNM4 → WU74YW98 → UPOKIFEA ⮌
17,536×(fixed) 1 node ⮎ ODD7VQQG ⮌
94 cycles1,340,134,818×(max) 21 nodes⮎ VOF6dWOF9 → XNG8dUNG7 → WPE6dWPE8 → XOIAdSLF7 → WND5dXQG8 → YPJ9dTKE6 → XPF5dXOE7 → YQJ9dTKD6 → XPG6dWNE7 → XQI8dULD7 → WPH7dVME8 → WOH7dVMF8 → WOG6dWNF8 → XOH7dVMF7 → WQG6dWND8 → XOJ9dTKF7 → WOE4dYPF8 → ZQI9dTLD5 → YQG7dVND6 → XRI9dTLC7 → WOH8dUMF8 ⮌
336,116,976×(fixed) 1 node ⮎ WOG7dVNF8 ⮌
854,386×(fixed) 1 node ⮎ XQJ6dWKD7 ⮌
420×(fixed) 1 node ⮎ KKJdddJJK ⮌
106 cycles6,710,925,752×(max) 103 nodes⮎ C9830caVUS → cXNLFNIG62 → aR872aWVC4 → YWPNEOGE76 → SPBA6WTSEC → QJHGASNMKE → IC750cYWRM → cTPF3ZOEA2 → aWJB8USK74 → WPMH0cMHE8 → cOB54YYSF2 → aUTH8UMA94 → WMLJ4YKIH8 → UO530caYFA → cXTK8UJA62 → aRMJ0cKHC4 → cWF50cYO72 → caTP8UEA32 → aXMJASKH64 → WRI50cYLC8 → cTOF2aOFA2 → aYJ98UUK54 → WTML0cIHA8 → cOJ52aYKF2 → aYT90cUA54 → cWTLIKIA72 → aPJ31baKE4 → aXWB0cS764 → cWRPGMEC72 → aPFB5XSOE4 → WSHB8USMB8 → OMHH4YMMHG → U8554YYYVA → UTTNJJGAAA → KJJ6ddWKKK → XKCddddQJ7 → WRKJ6WKJC8 → QOF10ccOFE → cbC98UUR22 → aZMLEOIH44 → WVA52aYT88 → YTONIKGFA6 → SJ971bWUKC → aPLG0cNIE4 → cWB72aWS72 → aYPPGMEE54 → WTBB5XSSA8 → SOJHGMMKFC → G9650cYXUO → cTRL7VICA2 → aOJF2aOKF4 → YW990cUU76 → cSPLKIIEB2 → aHB31baSM4 → aXWH4YM764 → WURP4YEC98 → UOLFASOIFA → KI992aUULK → YLL2ddaII6 → bXIFddNL63 → aXMF1bOH64 → aWR94YUC74 → WUPLEOIE98 → OLBA2aTSIG → YJH82aVMK6 → YSN50cYGB6 → cTSH6WMBA2 → aQJH4YMKD4 → WUD50cYQ98 → cTOLCQIFA2 → aJE92aUPK4 → YWLB0cSI76 → cSPH2aMEB2 → aYHB4YSM54 → WUTH4YMA98 → UOLJ4YKIFA → UK930caUJA → cXLK0cJI62 → caR30caC32 → caXXEO6632 → aXRR9TCC64 → WRKFEOOJC8 → OFA90cUTOG → cLJ97VUKI2 → aOL30caIF4 → cXW92aU762 → aYRPKIEC54 → WTFB1bSOA8 → aOJH8UMKF4 → WM950cYUH8 → cTOL4YIFA2 → aUJ92aUK94 → YWLL0cII76 → cSP32aaEB2 → aYXHASM654 → WTRI4YLCA8 → UOJF2aOKFA → YK990cUUJ6 → cSLL0cIIB2 → caH32aaM32 → aYXX4Y6654 → WUTRQCCA98 → OLJFDPOKIG ⮌
746,404,871×66 nodes⮎ MHG92aUNMI → YL753ZYWI6 → WTSP2aEBA8 → YOJHASMKF6 → SI950cYULC → cTLG2aNIA2 → aYJ72aWK54 → YWTP0cEA76 → cSPJASKEB2 → aIHB0cSML4 → cWH52aYM72 → aYTP4YEA54 → WUTJASKA98 → OLJI0cLKIG → c8330caaV2 → caXXMG6632 → aXRR5XCC64 → WSRFEOOCB8 → OHFA8UTOMG → MJ984YVUKI → UNL40cZIGA → cVK72aWJ82 → aYPN0cGE54 → cWTB6WSA72 → aQPJGMKED4 → WDB60cXSQ8 → cROHCQMFC2 → aFE94YUPO4 → WULB8USI98 → OMLH2aMIHG → Y8552aYYV6 → YTTSMGBAA6 → SJJH5XMKKC → SG510ccYNC → cbTG6WNA22 → aZQJ6WKD44 → WVQD0cQD88 → cONDCQQGF2 → aED96WUQP4 → WQLDASQID8 → OIDD2aQQLG → YDD82aVQQ6 → YSNDCQQGB6 → SHED6WQPMC → QGDB4YSQNE → UHDC6WRQMA → QKFD4YQOJE → UDC90cURQA → cLKFCQOJI2 → aE930caUP4 → cXWLASI762 → aRPI2aLEC4 → YWFB2aSO76 → YSPH8UMEB6 → SMHB4YSMHC → UHG54YYNMA → UTK74YWJAA → UPKJ0cKJEA → cKB10ccSJ2 → cbaH0cM322 → caZX4Y6432 → aXVUQC9864 → WRNLDPIGC8 → OFC72aWROG → YPF97VUOE6 → SOLB8USIFC ⮌
514,477,918×45 nodes⮎ KIHB0cSMLK → cH52ddaYM2 → bbXJBRK623 → ZYRG0cNC55 → cUTF6WOA92 → aQLJ8UKID4 → WMD30caQH8 → cXOD4YQF62 → aURD8UQC94 → WMLFCQOIH8 → OE952aYUPG → YTLB7VSIA6 → SOJH2aMKFC → YG950cYUN6 → cTSL6WIBA2 → aQJH2aMKD4 → YWD50cYQ76 → cTSPCQEBA2 → aJHEASPMK4 → WIB50cYSL8 → cTOH2aMFA2 → aYJ94YUK54 → WUTL0cIA98 → cOLJ2aKIF2 → aY930caU54 → cXWTKIA762 → aRPJ1bKEC4 → aWFB0cSO74 → cWPH8UME72 → aPMB4YSHE4 → WUHB4YSM98 → UOLH4YMIFA → UK952aYUJA → YTLK0cJIA6 → cSJ30caKB2 → caXH0cM632 → caXR4YC632 → aXUREOC964 → WRLF9TOIC8 → OKF92aUOJG → YL980cVUI6 → cSNL2aIGB2 → aYH72aWM54 → YWTP4YEA76 → USPJASKEBA ⮌
144,246,814×68 nodes⮎ 86552aYYXW → YTTRNFCAA6 → SJJF7VOKKC → OG910ccUNG → cbL86WVI22 → aZQN2aGD44 → YWVD6WQ876 → SQPNCQGEDC → GEDB6WSQPO → QHDB7VSQME → OHDC4YRQMG → UFD84YVQOA → UNKD8UQJGA → MKD70cWQJI → cPD40cZQE2 → caVDASQ832 → aXNICQLG64 → WRE72aWPC8 → YPOFASOFE6 → SIB98UUSLC → MLHG2aNMII → Y7542aZYW6 → YVTSOEBA86 → SNJH9TMKGC → KG750cYWNK → cTP6ddWEA2 → bXSI3ZLB63 → YWRH2aMC76 → YSPF4YOEB6 → USHB8USMBA → MKHH4YMMJI → U5540cZYYA → cVTTJJAA82 → aNJIddKKG4 → ZNI3ddZLG5 → aYJH1bMK54 → aWT50cYA74 → cWTPIKEA72 → aPJB1bSKE4 → aWHB0cSM74 → cWPH4YME72 → aUPB4YSE94 → WULHASMI98 → OLI52aYLIG → YT832aaVA6 → YXSNIKGB66 → SRH71bWMCC → aPGF4YONE4 → WUB96WUS98 → QOLLGMIIFE → C9632aaXUS → YXRLFNIC66 → SRF82aVOCC → YNGF8UONG6 → SM976WWUHC → QPLG4YNIEE → UCB72aWSRA → YPKHEOMJE6 → SBA50cYTSC → cTJHFNMKA2 → aJ850cYVK4 → cWTN0cGA72 → caPJ6WKE32 → aXQB0cSD64 → cWRHCQMC72 → aPFE4YPOE4 → WUBB8USS98 → OMLHGMMIHG ⮌
101,746,469×12 nodes⮎ K9830caVUK → cXNKddIG62 → bXMF2aOH63 → ZXR94YUC65 → VTRLEOICA9 → MJFA2aTOKI → YJ940cZUK6 → cVSL0cIB82 → caNH2aMG32 → aYX74YW654 → WUTROECA98 → OLJF9TOKIG ⮌
20,672×(fixed) 1 node ⮎ ODDD7VQQQG ⮌
11+---Not showing digit sets 11+ due to verbosity.