This is where I keep my functions, including hyperoperators.
Define BEAF(x) as the largest valid number using at most x symbols in BEAF. You can also define LAN(x) to use linear array notation only.
Subscripts are uncounted.
BEAF(1) = 9
BEAF(2) = 99
BEAF(3) = 9&9
BEAF(4) =? 9X&9 (9X = 9*X)
BEAF(5) =? X&X&9
Array of is very powerful for these.
BEAF(6) =? 9X&X&9
BEAF(7) =? {9,9-9} (ligion)
BEAF(8) =? {L,L}9,9
BEAF(26) >= {{L999,99}99,99&L,99}99,99 > Meameamealokkapoowa oompa
Let's get some examples with the LAN(n) function
LAN(1) = LAN(2) = 0
LAN(3) = {9} = 9
LAN(4) = {99} = 99
LAN(5) = {9,9} = 9^9
LAN(6) = {9,99} = 9^99Â
LAN(7) = {9,9,9} = Trienn
LAN(8) = {9,9,99}
LAN(9) = {9,9,9,9}
The LAN function follows a simple pattern.
{a,a,{a,a,{a,a,b}}}} = Dihyperaperiotion
{a,a,{a,a,{a,a,{a,a,b}}}} = Trihyperaperiotion
{a,a,a,b} = Aperionation
{a,a,a,a,b} = Aperiatotion
{a,a,a,a,a,b} = Aperiaguation
{a,b(1)2} = Iteration
{a,b,2(1)2} = Multiteration
{a,b,3(1)2} = Poweriteration
{a,b,4(1)2} = Tetraiteration
{a,a,b(1)2} = IteroaperiotionÂ
{a,b,1,2(1)2} = Iteroexpansion
{a,b,2,2(1)2} = Iteromultiexpansion
{a,b,1,3(1)2} = Iteroexplosion
{a,a,a,b(1)2} = Iteroaperionation
{a,b,1,1,2(1)2} = Iteromegotion
{a,b,1,1,1,2(1)2} = Iteroplaguation
{a,b(1)3} = Cuboiteration
{a,b(1)4} = Tesseroiteration
{a,a(1)b} = Aperioiteration
{a,b(1)1,2} = Expandoiteration
{a,b(1)2,2} = Multiexpandoiteration
{a,b(1)1,3} = Explodoiteration
{a,a(1)a,b} = Aperionoiteration
{a,b(1)1,1,2} = Megoiteration
{a,a(1)a,a,b} = Aperiatoiteration
{a,b(1)1,1,1,2} = Plaguoiteration
{a,b(1)(1)2} = Trioteration
{a,b(1)(1)3} = Cubotrioteration
{a,b(1)(1)1,2} = Expandotrioteration
{a,b(1)(1)(1)2} = Tetroteration
{a,b(1)(1)(1)(1)2} = Pentoteration
{a,b(2)2} = Trixxation
{a,b(2)3} = Cubotrixxation
{a,b(2)(1)2} = Iterotrixxation
{a,b(2)(2)2} = Triotrixxation
{a,b(3)2} = Texxation
{a,b(4)2} = Pexxation
{a,b(5)2} = Hexxitation ('it' added to distinguish from hexation)
{a,a(b)2} = Aperixxation
{a,b(0,1)2} = Dimensation
{a,b(0,1)(1)2} = Iterodimensation
{a,b(0,1)(2)2} = Trixxodimensation
{a,b(0,1)(0,1)2} = Triomensation
{a,b(0,1)(0,1)(0,1)2} = Tetromensation
{a,b(1,1)2} = Dimenunation
{a,b(2,1)2} = Dimenbiation
{a,b(3,1)2} = Dimentriation
{a,a(b,1)2} = Dimenaperation
{a,b(0,2)2} = Dimensexpation
{a,b(1,2)2} = Dimensexpixxation
{a,a(b,2)2} = Dimenaperixxation
{a,b(0,3)2} = Dimensexplation
{a,b(0,0,1)2} = Dimegonsation
{a,b(0,0,0,1)2} = Diplaguonsation
{a,b((1)1)2} = Trimensation
{a,b((0,1)1)2} = Termensation
{a,b(((1)1)1)2} = Penmensation
{a,b(X^^X)2} = Goppation
{a,b((X^^X)^X)2} = Goppafactation
{a,b(X^^X^2)2} = Boppation
{a,b(X^^X^3)2} = Troppation
{a,b(X^^X^X)2} = Goppatopation
{a,b(X^^X^^X)2} = Gopparxitration
{a,b(X^^X^^X^^X)2} = Gopparxitetation
{a,b(X^^^X)2} = Kungulation
{a,b(X^^^^X)2} = Quadrunculation
{a,b(X^^^^^X)2} = Quintunculation
{a,b({X,X,X})2} = Humongulation = Tri-entriculation
{a,b({X,X,X,X})2} = Tetro-entriculation
{a,b({X,X,X,X,X})2} = Pento-entriculation
{a,b({X,X(1)2})2} = Goobulation
{a,b({X,X(2)2})2} = Goopulation
{a,b({X,X(3)2})2} = Cubegulation
{a,b({X,X(X)2})2} = Golapulation
{a,b({X,X(0,0,1)2})2} = Bolapulation
{a,b({X,X(X^^X)2})2} = Goppatrixulation
{a,b({X,X({X,X,X})2})2} = Humongotrixulation
{a,b({X,X({X,X(X)2})2})2} = Golaputrixulation
{a,b({X,X({X,X({X,X(X)2})2})2})2} = Golaputrixotrixulation
{a,2/2} = a&a = Biarration
{a,3/2} = a&a&a = Triarration
{a,4/2} = Terarration
{a,5/2} = Penarration
{a,b/2} = Legislation = Aperioarration
{a,b,2/2} = Multilegislation
{a,b,3/2} = Powerlegislation
{a,a,b/2} = Legisoaperiotion
{a,b,1,2/2} = Legisoexpansion
{a,b,1,1,2/2} = Legisomegotion
{a,b(1)2/2} = Legisoiteration
{a,b(0,1)2/2} = Legisodimensation
{a,b((1)1)2/2} = Legisotrimensation
{a,b/3} = Cubolegislation
{a,b/4} = Tesserolegislation
{a,b/1,2} = Expandolegislation
{a,b/1,3} = Explodolegislation
{a,b/1,1,2} = Megolegislation
{a,b/1(1)2} = Iterolegislation
{a,b/1(0,1)2} = Dimensolegislation
{a,b/1/1/2} = Trigislation
{a,b/1/1/1/2} = Tergislation
{a,b(/1)2} = Legioteration
{a,b(/2)2} = Legiotraxxion
{a,b(/3)2} = Legiotetraxxion
{a,b(/0,1)2} = Legiodimation
{a,b//2} = Begislation
{a,b///2} = Tregislation
{a,b(1)/2} = Itergislation
{a,b(2)/2} = Trixxgislation
{a,b(0,1)/2} = Dimgislation
{a,b((1)1)/2} = Trimgislation
{a,b(X^^X)/2} = Goppagislation
{a,b(X^^^X)/2} = Kungugislation
{a,b({X,X,X})/2} = Humongislation
{a,b({X,X/2})/2} = {L,{X,X/2}}a,b = Legilegislation
{a,b({X,X(X,X/2)/2})/2} = {L,{L,{X,X/2}}X,X}a,b = Legilegilegislation
{L,L}a,b = Hyperlegislation
{L,{L,L}}a,b = Hyperhyperlegislation
{L,{L,{L,L}}}a,b = Hyperhyperhyperlegislation
{L,X,2}a,b = Superlegislation
{L,L,2}a,b = Legiontetration
{L,L,3}a,b = Legionpentation
{L,L,1,2}a,b = Legionexpansion
{L,L,L,L}a,b = Tetrentrico-legion
{L,L,L,L,L}a,b = Pententrico-legion
{L,L(1)2}a,b = Legioniteration
{L,L(2)2}a,b = Legiontrixxation
{L,L(3)2}a,b = Legiontexxation
{L,L(0,1)2}a,b = Legiondimensation
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{L,L(0,0,1)2}a,b = Legiondimegonsation
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{L,L((1)1)2}a,b = Legiontrimensation
{L,L(X^^X)2}a,b = Legiongoppation
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{L,L({L,})2}a,b = Legiongoppation
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it never ends, does it
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{a,b\2} = Lugislation
{a,b|2} = Lagislation
{a,b-2} = Ligislation
{a,b-2} = Ligislation
{LX}a,b = Apergislation
{LX}a,b = Apergislation
Yeah i'm not continuing this is stupidly ridiculously unfathomably boring.