| Radix Character Encoding | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V |
| W | X | Y | Z | a | b | c | d | e | f | g | h | i | j | k | l |
| m | n | o | p | q | r | s | t | u | v | w | x | y | z | Α | Β |
| Γ | Δ | Ε | Ζ | Η | Θ | Ι | Κ | Λ | Μ | Ν | Ξ | Ο | Π | Ρ | Σ |
| Τ | Υ | Φ | Χ | Ψ | Ω | α | β | γ | δ | ε | ζ | η | θ | ι | κ |
| Color Key | ||
|---|---|---|
| Orange | Fixed Point | number that becomes itself after one iteration |
| Green | Final Numbers | all numbers eventually reached, from all cycles |
| Purple | Cycle Start | iterations include entry into cycle, assuming it repeats |
| Red | Full Cycle | iterations include entire cycle, proving it repeats |
| Blue | Start Numbers | subset (optimization) of all numbers; minimal for full coverage |
| Gray | No Results | any calculation that has no results |
| Digits | # Full Cycles (excluding zero) |
Frequency | Cycle Length |
Full Cycles (excluding zero) (bold = exactly one cycle [excluding zero]) |
|---|---|---|---|---|
| 1 | 0 cycles | - | - | - |
| 2 | 2 cycles | 1,600× | (max) 10 nodes | ⮎ 1Σ → Π3 → Μ7 → ΔF → nV → HΒ → jZ → 9Κ → zJ → fd ⮌ |
| 1,600× | (max) 10 nodes | ⮎ 5Ξ → ΘB → vN → Xl → DΖ → rR → Pt → Tp → Lx → bh ⮌ | ||
| 3 | 1 cycle | 91,800× | (max) 2 nodes | ⮎ dΤf → eΤe ⮌ |
| 4 | 36 cycles | 74,438× | (max) 27 nodes | ⮎ TOtq → VMvo → ZIzk → hAΘc → x4ΞM → ΚahA → z6ΜK → ΖedE → r0ΣS → ΣOt2 → ΠUn4 → ΜIz8 → ΔgbG → n4ΞW → ΚGΒA → zkXK → fCΖe → t0ΣQ → ΣSp2 → ΠMv4 → ΜYj8 → ΔAΘG → xmVM → bGΒi → l6ΜY → ΖCΖE → tqRQ ⮌ |
| 69,871× | (max) 27 nodes | ⮎ R0Σs → ΣQr2 → ΠQr4 → ΜQr8 → ΔQrG → nQrW → RGΒs → lQrY → RCΖs → tQrQ → TQrq → RMvs → ZQrk → RAΘs → xQrM → bQri → R6Μs → ΖQrE → rQrS → ROts → VQro → RIzs → hQrc → R4Ξs → ΚQrA → zQrK → fQre ⮌ | ||
| 69,475× | (max) 27 nodes | ⮎ 96ΜΛ → ΖΑHE → riZS → P8Κu → ΒUnI → jIza → h8Κc → Β4ΞI → ΚiZA → z8ΚK → ΒedI → j0Σa → Σ8Κ2 → ΠΑH4 → ΜiZ8 → Δ8ΚG → ΒmVI → jGΒa → l8ΚY → ΒCΖI → tiZQ → T8Κq → ΒMvI → jYja → B8ΚΙ → ΒwLI → jaha ⮌ | ||
| 69,445× | (max) 27 nodes | ⮎ 52ΠΟ → ΞΙ96 → ΘyJC → vedO → X0Σm → ΣEΔ2 → ΠoT4 → ΜKx8 → ΔcfG → n2ΠW → ΞGΒ6 → ΘkXC → vCΖO → tWlQ → TEΔq → pMvU → ZKxk → dAΘg → x2ΠM → Ξah6 → Θ6ΜC → ΖuNE → rWlS → PEΔu → pUnU → LIzy → hcfc ⮌ | ||
| 69,279× | (max) 27 nodes | ⮎ 72ΠΝ → ΞΕD6 → ΘqRC → vOtO → XUnm → JEΔΑ → pgbU → L4Ξy → ΚcfA → z2ΠK → Ξed6 → Θ0ΣC → ΣuN2 → ΠWl4 → ΜEΔ8 → ΔoTG → nKxW → dGΒg → l2ΠY → ΞCΖ6 → ΘsPC → vSpO → XMvm → ZEΔk → pAΘU → xKxM → dahg ⮌ | ||
| 68,995× | (max) 27 nodes | ⮎ 30ΣΡ → ΣΝ52 → ΠΗB4 → ΜuN8 → ΔWlG → nEΔW → pGΒU → lKxY → dCΖg → t2ΠQ → ΞSp6 → ΘMvC → vYjO → XAΘm → xEΔM → pahU → L6Μy → ΖcfE → r2ΠS → ΞOt6 → ΘUnC → vIzO → hWlc → F4ΞΕ → ΚoTA → zKxK → fcfe ⮌ | ||
| 68,683× | (max) 27 nodes | ⮎ FCΖΕ → toTQ → TKxq → dMvg → Z2Πk → ΞAΘ6 → ΘwLC → vahO → X6Μm → ΖEΔE → roTS → PKxu → dUng → J2ΠΑ → Ξgb6 → Θ4ΞC → ΚuNA → zWlK → fEΔe → p0ΣU → ΣKx2 → Πcf4 → Μ2Π8 → ΞΓF6 → ΘmVC → vGΒO → lWlY ⮌ | ||
| 68,665× | (max) 27 nodes | ⮎ D2ΠΗ → ΞsP6 → ΘSpC → vMvO → ZWlk → FAΘΕ → xoTM → bKxi → d6Μg → Ζ2ΠE → ΞqR6 → ΘOtC → vUnO → XIzm → hEΔc → p4ΞU → ΚKxA → zcfK → f2Πe → Ξ0Σ6 → ΣΗB2 → ΠuN4 → ΜWl8 → ΔEΔG → pmVU → LGΒy → lcfY ⮌ | ||
| 68,539× | (max) 27 nodes | ⮎ 94ΞΛ → ΚΑHA → ziZK → f8Κe → Β0ΣI → ΣiZ2 → Π8Κ4 → ΜΑH8 → ΔiZG → n8ΚW → ΒGΒI → liZY → D8ΚΗ → ΒsPI → jSpa → N8Κw → ΒYjI → jAΘa → x8ΚM → ΒahI → j6Μa → Ζ8ΚE → ΒqRI → jOta → V8Κo → ΒIzI → jgba ⮌ | ||
| 67,265× | (max) 27 nodes | ⮎ B2ΠΙ → ΞwL6 → ΘahC → v6ΜO → ΖWlE → rEΔS → pOtU → VKxo → dIzg → h2Πc → Ξ4Ξ6 → ΚΗBA → zuNK → fWle → F0ΣΕ → ΣoT2 → ΠKx4 → Μcf8 → Δ2ΠG → ΞmV6 → ΘGΒC → vkXO → XCΖm → tEΔQ → pSpU → NKxw → dYjg ⮌ | ||
| 66,914× | (max) 27 nodes | ⮎ D4ΞΗ → ΚsPA → zSpK → fMve → Z0Σk → ΣAΘ2 → ΠwL4 → Μah8 → Δ6ΜG → ΖmVE → rGΒS → lOtY → VCΖo → tIzQ → hSpc → N4Ξw → ΚYjA → zAΘK → xedM → b0Σi → Σ6Μ2 → ΠΕD4 → ΜqR8 → ΔOtG → nUnW → JGΒΑ → lgbY ⮌ | ||
| 66,680× | (max) 27 nodes | ⮎ B6ΜΙ → ΖwLE → rahS → P6Μu → ΖUnE → rIzS → hOtc → V4Ξo → ΚIzA → zgbK → f4Ξe → Κ0ΣA → ΣyJ2 → Πed4 → Μ0Σ8 → ΣΓF2 → ΠmV4 → ΜGΒ8 → ΔkXG → nCΖW → tGΒQ → lSpY → NCΖw → tYjQ → TAΘq → xMvM → bYji ⮌ | ||
| 66,617× | (max) 27 nodes | ⮎ HEΔΓ → pkXU → LCΖy → tcfQ → T2Πq → ΞMv6 → ΘYjC → vAΘO → xWlM → bEΔi → p6ΜU → ΖKxE → rcfS → P2Πu → ΞUn6 → ΘIzC → vgbO → X4Ξm → ΚEΔA → zoTK → fKxe → d0Σg → Σ2Π2 → ΠΝ54 → ΜΗB8 → ΔuNG → nWlW ⮌ | ||
| 66,201× | (max) 27 nodes | ⮎ H2ΠΓ → ΞkX6 → ΘCΖC → vsPO → XSpm → NEΔw → pYjU → LAΘy → xcfM → b2Πi → Ξ6Μ6 → ΘΕDC → vqRO → XOtm → VEΔo → pIzU → hKxc → d4Ξg → Κ2ΠA → ΞyJ6 → ΘedC → v0ΣO → ΣWl2 → ΠEΔ4 → ΜoT8 → ΔKxG → ncfW ⮌ | ||
| 66,127× | (max) 27 nodes | ⮎ 90ΣΛ → ΣΑH2 → ΠiZ4 → Μ8Κ8 → ΔΑHG → niZW → H8ΚΓ → ΒkXI → jCΖa → t8ΚQ → ΒSpI → jMva → Z8Κk → ΒAΘI → xiZM → b8Κi → Β6ΜI → ΖiZE → r8ΚS → ΒOtI → jUna → J8ΚΑ → ΒgbI → j4Ξa → Κ8ΚA → ΒyJI → jeda ⮌ | ||
| 65,948× | (max) 27 nodes | ⮎ D0ΣΗ → ΣsP2 → ΠSp4 → ΜMv8 → ΔYjG → nAΘW → xGΒM → lahY → D6ΜΗ → ΖsPE → rSpS → PMvu → ZUnk → JAΘΑ → xgbM → b4Ξi → Κ6ΜA → ΖyJE → redS → P0Σu → ΣUn2 → ΠIz4 → Μgb8 → Δ4ΞG → ΚmVA → zGΒK → ledY ⮌ | ||
| 65,888× | (max) 27 nodes | ⮎ DAΘΗ → xsPM → bSpi → N6Μw → ΖYjE → rAΘS → xOtM → bUni → J6ΜΑ → ΖgbE → r4ΞS → ΚOtA → zUnK → fIze → h0Σc → Σ4Ξ2 → ΠΙ94 → ΜyJ8 → ΔedG → n0ΣW → ΣGΒ2 → ΠkX4 → ΜCΖ8 → ΔsPG → nSpW → NGΒw → lYjY ⮌ | ||
| 65,870× | (max) 27 nodes | ⮎ B4ΞΙ → ΚwLA → zahK → f6Μe → Ζ0ΣE → ΣqR2 → ΠOt4 → ΜUn8 → ΔIzG → ngbW → H4ΞΓ → ΚkXA → zCΖK → tedQ → T0Σq → ΣMv2 → ΠYj4 → ΜAΘ8 → ΔwLG → nahW → H6ΜΓ → ΖkXE → rCΖS → tOtQ → VSpo → NIzw → hYjc ⮌ | ||
| 65,750× | (max) 27 nodes | ⮎ 74ΞΝ → ΚΕDA → zqRK → fOte → V0Σo → ΣIz2 → Πgb4 → Μ4Ξ8 → ΚΓFA → zmVK → fGΒe → l0ΣY → ΣCΖ2 → ΠsP4 → ΜSp8 → ΔMvG → nYjW → HAΘΓ → xkXM → bCΖi → t6ΜQ → ΖSpE → rMvS → ZOtk → VAΘo → xIzM → hahc ⮌ | ||
| 65,498× | (max) 27 nodes | ⮎ 50ΣΟ → ΣΙ92 → ΠyJ4 → Μed8 → Δ0ΣG → ΣmV2 → ΠGΒ4 → ΜkX8 → ΔCΖG → tmVQ → TGΒq → lMvY → ZCΖk → tAΘQ → xSpM → bMvi → Z6Μk → ΖAΘE → xqRM → bOti → V6Μo → ΖIzE → rgbS → P4Ξu → ΚUnA → zIzK → hedc ⮌ | ||
| 65,449× | (max) 27 nodes | ⮎ F6ΜΕ → ΖoTE → rKxS → dOtg → V2Πo → ΞIz6 → ΘgbC → v4ΞO → ΚWlA → zEΔK → pedU → L0Σy → Σcf2 → Π2Π4 → ΞΛ76 → ΘΓFC → vmVO → XGΒm → lEΔY → pCΖU → tKxQ → dSpg → N2Πw → ΞYj6 → ΘAΘC → xuNM → bWli ⮌ | ||
| 65,204× | (max) 27 nodes | ⮎ HCΖΓ → tkXQ → TCΖq → tMvQ → ZSpk → NAΘw → xYjM → bAΘi → x6ΜM → ΖahE → r6ΜS → ΖOtE → rUnS → PIzu → hUnc → J4ΞΑ → ΚgbA → z4ΞK → ΚedA → z0ΣK → Σed2 → Π0Σ4 → ΣΛ72 → ΠΓF4 → ΜmV8 → ΔGΒG → nkXW ⮌ | ||
| 64,655× | (max) 27 nodes | ⮎ TMvq → ZMvk → ZAΘk → xAΘM → xahM → b6Μi → Ζ6ΜE → ΖqRE → rOtS → VOto → VIzo → hIzc → h4Ξc → Κ4ΞA → ΚyJA → zedK → f0Σe → Σ0Σ2 → ΣΟ32 → ΠΛ74 → ΜΓF8 → ΔmVG → nGΒW → lGΒY → lCΖY → tCΖQ → tSpQ ⮌ | ||
| 64,400× | (max) 27 nodes | ⮎ 70ΣΝ → ΣΕD2 → ΠqR4 → ΜOt8 → ΔUnG → nIzW → hGΒc → l4ΞY → ΚCΖA → zsPK → fSpe → N0Σw → ΣYj2 → ΠAΘ4 → ΜwL8 → ΔahG → n6ΜW → ΖGΒE → rkXS → PCΖu → tUnQ → TIzq → hMvc → Z4Ξk → ΚAΘA → zwLK → fahe ⮌ | ||
| 64,268× | (max) 27 nodes | ⮎ H0ΣΓ → ΣkX2 → ΠCΖ4 → ΜsP8 → ΔSpG → nMvW → ZGΒk → lAΘY → xCΖM → tahQ → T6Μq → ΖMvE → rYjS → PAΘu → xUnM → bIzi → h6Μc → Ζ4ΞE → ΚqRA → zOtK → fUne → J0ΣΑ → Σgb2 → Π4Ξ4 → ΜΙ98 → ΔyJG → nedW ⮌ | ||
| 63,890× | (max) 27 nodes | ⮎ B0ΣΙ → ΣwL2 → Πah4 → Μ6Μ8 → ΖΓFE → rmVS → PGΒu → lUnY → JCΖΑ → tgbQ → T4Ξq → ΚMvA → zYjK → fAΘe → x0ΣM → Σah2 → Π6Μ4 → ΜΕD8 → ΔqRG → nOtW → VGΒo → lIzY → hCΖc → t4ΞQ → ΚSpA → zMvK → fYje ⮌ | ||
| 23,937× | 9 nodes | ⮎ XKxm → dEΔg → p2ΠU → ΞKx6 → ΘcfC → v2ΠO → ΞWl6 → ΘEΔC → voTO ⮌ | ||
| 21,057× | 9 nodes | ⮎ XEΔm → pEΔU → pKxU → dKxg → d2Πg → Ξ2Π6 → ΞΗB6 → ΘuNC → vWlO ⮌ | ||
| 21,057× | 9 nodes | ⮎ L2Πy → Ξcf6 → Θ2ΠC → ΞuN6 → ΘWlC → vEΔO → pWlU → LEΔy → pcfU ⮌ | ||
| 21,057× | 9 nodes | ⮎ F2ΠΕ → ΞoT6 → ΘKxC → vcfO → X2Πm → ΞEΔ6 → ΘoTC → vKxO → dWlg ⮌ | ||
| 20,817× | 9 nodes | ⮎ R2Πs → ΞQr6 → ΘQrC → vQrO → XQrm → REΔs → pQrU → RKxs → dQrg ⮌ | ||
| 20,745× | 9 nodes | ⮎ 92ΠΛ → ΞΑH6 → ΘiZC → v8ΚO → ΒWlI → jEΔa → p8ΚU → ΒKxI → jcfa ⮌ | ||
| 20,745× | 9 nodes | ⮎ F8ΚΕ → ΒoTI → jKxa → d8Κg → Β2ΠI → ΞiZ6 → Θ8ΚC → ΒuNI → jWla ⮌ | ||
| 20,745× | 9 nodes | ⮎ L8Κy → ΒcfI → j2Πa → Ξ8Κ6 → ΘΑHC → viZO → X8Κm → ΒEΔI → piZU ⮌ | ||
| 8,091× | 3 nodes | ⮎ j8Κa → Β8ΚI → ΒiZI ⮌ | ||
| 7,155× | 3 nodes | ⮎ R8Κs → ΒQrI → jQra ⮌ | ||
| 5 | 1 cycle | 32,801,436× | (fixed) (max) 1 node | ⮎ sQΤrR ⮌ |
| 6 | 2 cycles | 331,311,981× | (max) 28 nodes | ⮎ HD5ΝΖΓ → ΘskXQC → vSCΖqO → tXNulQ → XTDΕpm → rMEΔwS → paOtiU → VL7Λxo → ΔcIzgG → nh3ΟbW → ΜH5ΝΒ8 → ΘΔjYFC → voAΘUO → xXJylM → fbDΕhe → r60ΣΝS → ΣΗOtC2 → ΠuUnO4 → ΜWIzm8 → ΔhFΓbG → om5ΝWV → ΘJFΓzC → vnfcVO → XI2ΠΑm → ΞiEΔa6 → Θp7ΛTC → ΔvLwNG → nbXkhW ⮌ |
| 138,843,015× | 27 nodes | ⮎ F4ΤΤΞΕ → ΟΔ8ΚF5 → ΚΒnUHA → zkIzYK → hfBΗdc → v51ΡΞO → ΠΙWlA4 → ΜyEΔK8 → ΔpdeTG → nM0ΣwW → ΣaGΒi2 → Πl7ΛX4 → ΜΔDΕF8 → ΔrnURG → nQIzsW → hSGΒqc → lO4ΞuY → ΚWCΖmA → ztFΓPK → nfTodW → LH1ΡΒy → ΠkcfY4 → ΜC2ΠΗ8 → ΞΔtOF6 → ΘoUnUC → vKIzyO → heWlec ⮌ | ||
| 7 | 3 cycles | 4,821,719,226× | 2 nodes | ⮎ yfJΤydL → zdKΤxfK ⮌ |
| 522,394,347× | 2 nodes | ⮎ zfIΤzdK → ΑfLΤwdJ ⮌ | ||
| 499,242,303× | (max) 4 nodes | ⮎ xdIΤzfM → ΑdJΤyfJ → zhKΤxbK → yfLΤwdL ⮌ | ||
| 8+ | - | - | - | Not showing digit sets 8+ due to verbosity. |