Numbers from Bird's array notation
This page contains numbers from Bird's array notation. Note that the numbers will start from multidimensional array notation, as linear array notation numbers are basically identical to the ones in BEAF.
Without further ado, let's begin the naming scheme.
Bird's multidimensional array numbers
(note: it works similar with BEAF, by changing [n] to (n-1) for n-1 dimensional array)
From [2] to [3]
dwoogol = {10,100[2]2} (equal to goobol, {10,100(1)2} in BEAF)
dwoogolplex = {10,dwoogol[2]2} (equal to goobolplex, {10,goobol(1)2} in BEAF)
dwoogolduplex = {10,dwoogolplex[2]2} (equal to goobolduplex, {10,goobolplex(1)2} in BEAF)
dwiggol = {10,100,2[2]2} (equal to gibbol, {10,100,2(1)2} in BEAF)
dwaggol = {10,100,3[2]2} (equal to gabbol, {10,100,3(1)2} in BEAF)
dweegol = {10,100,4[2]2} (equal to geebol, {10,100,4(1)2} in BEAF)
dwigol = {10,100,5[2]2} (equal to gibol, {10,100,5(1)2} in BEAF)
dwoggol = {10,100,6[2]2} (equal to gobbol, {10,100,6(1)2} in BEAF)
dwagol = {10,100,7[2]2} (equal to gabol, {10,100,7(1)2} in BEAF)
dwoboogol = {10,10,100[2]2} (equal to boobol, {10,10,100(1)2} in BEAF)
dwobiggol = {10,10,100,2[2]2} (equal to bibbol, {10,10,100,2(1)2} in BEAF)
dwobaggol = {10,10,100,3[2]2} (equal to bibbol, {10,10,100,3(1)2} in BEAF)
dwobeegol = {10,10,100,4[2]2} (equal to beebol, {10,10,100,4(1)2} in BEAF)
dwobigol = {10,10,100,5[2]2} (equal to beebol, {10,10,100,5(1)2} in BEAF)
dwotroogol = {10,10,10,100[2]2} (equal to troobol, {10,10,10,100(1)2} in BEAF)
dwoquadroogol = {10,10,10,10,100[2]2} (equal to quadroobol, {10,10,10,10,100(1)2} in BEAF)
dwoquintoogol = {10,10,10,10,10,100[2]2} (equal to quadroobol, {10,10,10,10,100(1)2} in BEAF)
latri = {3,3[2]3} (= {3,3(1)3} in BEAF)
dual-decal = {10,10[2]3}
gootrol = {10,100[2]3} (= {10,100(1)3} in BEAF)
gooquadrol = {10,100[2]4} (= {10,100(1)4} in BEAF)
gossol = {10,10[2]100}
gissol = {10,10[2]100,2}
gassol = {10,10[2]100,3}
geesol = {10,10[2]100,4}
gussol = {10,10[2]100,5}
mossol = {10,10[2]10,100}
bossol = {10,10[2]10,10,100}
trossol = {10,10[2]10,10,10,100}
dubol = {10,100[2]1[2]2}
lower dimentri = {3,3[3]2}
dossol = {10,10[2]1[2]100}
xappol = {10,10[3]2}
From [3] to [1,2]
goxxol = {10,100[3]2}
grand xappol = {10,10[3]3}
moxxol = {10,10[3]100}
mixxol = {10,10[3]100,2}
maxxol = {10,10[3]100,3}
mexxol = {10,10[3]100,4}
muxxol = {10,10[3]100,5}
goxxol-by-goobol = {10,100[3]1[2]2}
multidimensional drib = {10,10[2]10,10[3]1[2]2}
goxxol-by-dubol = {10,100[3]1[2]1[2]2}
deutero-goxxol = {10,100[3]1[3]2}
trito-goxxol = {10,100[3]1[3]1[3]2}
lower dimentet = {4,4[4]2}
colossol = {10,10[4]2}
coloxxol = {10,100[4]2}
grand colossol = {10,10[4]3}
multidimensional apprehendere = {4, 3 [4] 1 [3] 1 [2] 1, 1, 1, 6} (number mentioned in a multi-dimensional pdf file)
deutero-coloxxol = {10,100[4]1[4]2}
suboptimal multidimensional apprehendere = {17,17 [4] 1 [4] 1 [2] 1 [2] 1 [2] 2}
lower dimenpent = {5,5[5]2}
terossol = {10,10[5]2}
teroxxol = {10,100[5]2}
deutero-teroxxol = {10,100[5]1[5]2}
petossol = {10,10[6]2}
petoxxol = {10,100[6]2}
ectossol = {10,10[7]2}
ectoxxol = {10,100[7]2}
lower dimenoct = {8,8[8]2}
zettossol = {10,10[8]2}
zettoxxol = {10,100[8]2}
yottossol = {10,10[9]2}
yottoxxol = {10,100[9]2}
lower dimendecal / ditasol / ronnossol = {10,10[10]2} (in BEAF, {10,10(9)2})
ronnoxxol = {10,100[10]2}
rannygazoo dimensional array = {52,67 [5] 5 [10] 2}
gomgathor = {10,100[1,2]2}
gongulus = {10,10[101]2}
Cumulative numbers: 67
Hyperdimensional array numbers
Note that BEAF and Bird's array notation are no longer exact at this point.
From [1,2] to [1,1,2]
gomgathorplex = {10,gomgathor[1,2]2}
gimgathor = {10,100,2[1,2]2}
gamgathor = {10,100,3[1,2]2}
geemgathor = {10,100,4[1,2]2}
gimgathor = {10,100,5[1,2]2}
gommgathor = {10,100,6[1,2]2}
gammgathor = {10,100,7[1,2]2}
bomgathor = {10,10,100[1,2]2}
bomgathorgong = {10,10,100000[1,2]2}
tromgathor = {10,10,10,100[1,2]2}
quadromgathor = {10,10,10,10,100[1,2]2}
quintomgathor = {10,10,10,10,10,100[1,2]2}
goobomgathor = {10,100[2]2[1,2]2}
gootromgathor = {10,100[2]3[1,2]2}
gossomgathor = {10,10[2]100[1,2]2}
dubomgathor = {10,10[2]1[2]2[1,2]2}
goxlomgathor / goxxol-carta-gongulus = {10,100[3]2[1,2]2}
coloxlomgathor / coloxxol-carta-gongulus = {10,100[4]2[1,2]2}
teroxlomgathor = {10,100[5]2[1,2]2}
petoxlomgathor = {10,100[6]2[1,2]2}
cosmatri = {10,10[1,2]3}
gomtrigathor = {10,100[1,2]3}
cosmatet = {10,10[1,2]4}
gomtergathor = {10,100[1,2]4}
gompeggathor = {10,100[1,2]5}
gomhexgathor = {10,100[1,2]6}
gomhepgathor = {10,100[1,2]7}
gomocgathor = {10,100[1,2]8}
gomenngathor = {10,100[1,2]9}
gomdekgathor = {10,100[1,2]10}
perestroika hyperdimension = {10,140[1,2]22}
gossogathor = {10,10[1,2]100}
gissogathor = {10,10[1,2]100,2}
gassogathor = {10,10[1,2]100,3}
geesogathor = {10,10[1,2]100,4}
gussogathor = {10,10[1,2]100,5}
bracket array hyperal = {10,10[1,2]10,10}
mossogathor = {10,10[1,2]10,100}
missogathor = {10,10[1,2]10,100,2}
massogathor = {10,10[1,2]10,100,3}
meesogathor = {10,10[1,2]10,100,4}
mussogathor = {10,10[1,2]10,100,5}
bracket array trihyperal = {10,10[1,2]10,10,10}
bossogathor = {10,10[1,2]10,10,100}
trossogathor = {10,10[1,2]10,10,10,100}
gomgathor-by-goobol = {10,100[1,2]1[2]2}
gomgathor-by-gossol = {10,10[1,2]1[2]100}
gomgathor-by-mossol = {10,10[1,2]1[2]10,100}
gomgathor-by-bossol = {10,10[1,2]1[2]10,10,100}
gomgathor-by-dubol = {10,100[1,2]1[2]1[2]2}
gomgathor-by-triubol = {10,100[1,2]1[2]1[2]1[2]2}
gomgathor-by-goxxol = {10,100[1,2]1[3]2}
gomgathor-by-goxxol-by-goobol = {10,100[1,2]1[3]1[2]2}
gomgathor-by-deutero-goxxol = {10,100[1,2]1[3]1[3]2}
gomgathor-by-trito-goxxol = {10,100[1,2]1[3]1[3]1[3]2}
gomgathor-by-coloxxol = {10,100[1,2]1[4]2}
gomgathor-by-teroxxol = {10,100[1,2]1[5]2}
deutero-gomgathor = {10,100[1,2]1[1,2]2}
trito-gomgathor = {10,100[1,2]1[1,2]1[1,2]2}
teterto-gomgathor = {10,100[1,2]1[1,2]1[1,2]1[1,2]2}
gomgathorfact = {10,100[2,2]2}
grand gomgathorfact / gomgathorfactiplex = {10,gomgathorfact[2,2]2}
gomtrigathorfact = {10,100[2,2]3}
gossogathorfact = {10,10[2,2]100}
agitato cuatro = {16,16[2,2]1[2]2}
deutero-gomgathorfact = {10,100[2,2]1[2,2]2}
gomgathordoublefact = {10,100[3,2]2}
gomgathortriplefact = {10,100[4,2]2}
gomgathorquadruplefact = {10,100[5,2]2}
gomgathorquintuplefact = {10,100[6,2]2}
gomgathorduo = {10,100[1,3]2}
gomgathorduofact = {10,100[2,3]2}
gomgathorduodoublefact = {10,100[3,3]2}
gomgathorduotriplefact = {10,100[4,3]2}
gomgathorduoquadruplefact = {10,100[5,3]2}
gomgathortrio = {10,100[1,4]2}
gomgathortriofact = {10,100[2,4]2}
gomgathorquad = {10,100[1,5]2}
gomgathorpent = {10,100[1,6]2}
gomgathorhex = {10,100[1,7]2}
gomgathorsept = {10,100[1,8]2}
gomgathoroct = {10,100[1,9]2}
gomgathorenn = {10,100[1,10]2}
gomgathordeck = {10,100[1,11]2}
Cumulative numbers: 144
From [1,1,2] to [1,1,1,2]
damgathor = {10,100[1,1,2]2}
damgathorfact = {10,100[2,1,2]2}
damgathordoublefact = {10,100[3,1,2]2}
damgathortriplefact = {10,100[4,1,2]2}
damgomgathgathor = {10,100[1,2,2]2}
damgomgathorfactgathor = {10,100[2,2,2]2}
damgomgathordoublefactgathor = {10,100[3,2,2]2}
damgomgathorduodoublefactgathor = {10,100[4,2,2]2}
damgomgathorduogathor = {10,100[1,3,2]2}
damgomgathortriogathor = {10,100[1,4,2]2}
damgathorduo = {10,100[1,1,3]2}
damgathorduofact = {10,100[2,1,3]2}
damgomgathorduo = {10,100[1,2,3]2}
damgathortrio = {10,100[1,1,4]2}
damgathorquad = {10,100[1,1,5]2}
damgathorpent = {10,100[1,1,6]2}
wole whole = {169,150[2,6,6]2}
damgathorhex = {10,100[1,1,7]2}
damgathorsept = {10,100[1,1,8]2}
tramgathor = {10,100[1,1,1,2]2}
tramgathorduo = {10,100[1,1,1,3]2}
tetramgathor = {10,100[1,1,1,1,2]2}
pentamgathor = {10,100[1,1,1,1,1,2]2}
hexamgathor = {10,100[1,1,1,1,1,1,2]2}
heptamgathor = {10,100[1,1,1,1,1,1,1,2]2}
octamgathor = {10,100[1,1,1,1,1,1,1,1,2]2}
ennamgathor = {10,100[1,1,1,1,1,1,1,1,1,2]2}
dekamgathor = {10,100[1,1,1,1,1,1,1,1,1,1,2]2}
Nested array numbers
gomtresor / gomtothol (combining go- with tres, which means 3 in Spanish (trimensional)) = {10,100[1[1]2]2}
gomtresorfact / gomtotholfact = {10,100[2[1]2]2}
gomgathtresor = {10,100[1,2[1]2]2}
damgathtresor = {10,100[1,1,2[1]2]2}
tramgathtresor = {10,100[1,1,1,2[1]2]2}
tetramgathtresor = {10,100[1,1,1,1,2[1]2]2}
gomtresorduo = {10,100[1[1]3]2}
gomtresortrio = {10,100[1[1]4]2}
gomtresorquad = {10,100[1[1]5]2}
hyper-gomgathorfact = {10,100[1[1]1,2]2}
hyper-deutero-gomgathorfact = {10,100[1[1]2,2]2}
hyper-trito-gomgathorfact = {10,100[1[1]3,2]2}
hyper-gomgathordoublefact = {10,100[1[1]1,1,2]2}
hyper-gomgathortriplefact = {10,100[1[1]1,1,1,2]2}
damtresor / gramtothol = {10,100[1[2]2]2}
hyper-gramgathorfact = {10,100[1[2]1,2]2}
tramtresor / thramtothol = {10,100[1[3]2]2}
quadramtresor / tetramtresor / terimtothol = {10,100[1[4]2]2}
pentamtresor / pentamtothol = {10,100[1[5]2]2}
hexamtresor = {10,100[1[6]2]2}
heptamtresor = {10,100[1[7]2]2}
octamtresor = {10,100[1[8]2]2}
ennamtresor = {10,100[1[9]2]2}
dekamtresor = {10,100[1[10]2]2}
gomcuatror / gomtertol (combining go- with cuatro, which means 4 in Spanish (quadramensional)) = {10,100[1[1,2]2]2}
gomcincor (combining go- with cinco, which means 5 in Spanish (quintamensional)) / gomtopol = {10,100[1[1[1]2]2]2}
gomseisor / gomhathor = {10,100[1[1[1,2]2]2]2}
gomsietor / gomheptol = {10,100[1[1[1[1]2]2]2]2}
gomochor / gomoctol = {10,100[1[1[1[1,2]2]2]2]2}
gomnovor / gomentol = {10,100[1[1[1[1[1]2]2]2]2]2}
gomdiecor / gomdekathol = {10,100[1[1[1[1[1,2]2]2]2]2]2}
backslashed decal / backoogol = {10,10[1\2]2} (from backslash-googol)
Cumulative numbers: 204
Beyond nested array numbers (up to 1\1\2)
backoogolplex = {10,3,2[1\2]2}
backiggol = {10,10,2[1\2]2}
backaggol = {10,10,3[1\2]2}
backugold = {10,10,10[1\2]2}
backugolthra = {10,10,10,2[1\2]2}
backotroogol = {10,10,10,10[1\2]2}
backoquadroogol = {10,10,10,10,10[1\2]2}
backogoobol = {10,10[2]2[1\2]2}
backogomgathor = {10,10[1,2]2[1\2]2}
backogomtothol = {10,10[1[1]2]2[1\2]2}
backogomtertol = {10,10[1[1,2]2]2[1\2]2}
backoogotri = {10,10[1\2]3}
backoogotet = {10,10[1\2]4}
backoogopent = {10,10[1\2]5}
backoogoboogol = {10,10[1\2]10}
backoogol-by-troogol = {10,10[1\2]10,100}
backoogol-by-quadoogol = {10,10[1\2]10,10,100}
double-backoogol / deutero-backoogol = {10,10[1\2]1[1\2]2}
triple-backoogol / trito-backoogol = {10,10[1\2]1[1\2]1[1\2]2}
quadruple-backoogol / teterto-backoogol = {10,10[1\2]1[1\2]1[1\2]1[1\2]2}
backoodugol / backoogolfact = {10,10[2\2]2}
double-backoodugol = {10,10[2\2]1[2\2]2}
triple-backoodugol = {10,10[2\2]1[2\2]1[2\2]2}
backootrigol = {10,10[3\2]2}
backoohyperol = {10,10[1,2\2]2}
backoo-hypertriol = {10,10[1,3\2]2}
backoo-hypertetrol = {10,10[1,4\2]2}
backoo-deuterhyperol = {10,10[1,1,2\2]2}
backoo-deuterhypertriol = {10,10[1,1,3\2]2}
backoo-tritohyperol = {10,10[1,1,2\2]2}
backoo-dimensol = {10,10[1[2]2\2]2}
backoo-gomgathor = {10,10[1[1,2]2\2]2}
backoo-gomtresor / backoo-gomtothol = {10,10[1[1[1]2]2\2]2}
backoo-gomcuatror / backoo-gomtertol = {10,10[1[1[1,2]2]2\2]2}
backoo-gomcincor / backoo-gomtopol = {10,10[1[1[1[1]2]2]2\2]2}
backoo-backoogol / dulinserted-backoogol = {10,10[1[1\2]2\2]2}
backoo-backoodugol / dulinserted-backoogol = {10,10[1[2\2]2\2]2}
backoo-backoomegol / backoo-backoo-hyperol = {10,10[1[1,2\2]2\2]2}
dubackoo-dimensol / backoo-backoo-dimensol = {10,10[1[1[2]2\2]2\2]2}
backoo-backoo-gomgathor / backoo-backoo-gomgathor = {10,10[1[1[1,2]2\2]2\2]2}
dubackoo-gomtothol / backoo-backoo-gomtothol = {10,10[1[1[1[2]2]2\2]2\2]2}
dubackoo-gomtertol / backoo-backoo-gomtertol = {10,10[1[1[1[1,2]2]2\2]2\2]2}
trilinserted-backoogol = {10,10[1[1[1\2]2\2]\2]2}
tetrinserted-backoogol = {10,10[1[1[1[1\2]2\2]2\2]\2]2}
terrible backoogol = {10,10[1\3]2}
terrible backoodugol = {10,10[2\3]2}
terrible backootrigol = {10,10[3\3]2}
terrible backoohyperol = {10,10[1,2\3]2}
terrible backoohypertriol = {10,10[1,3\3]2}
terrible backoodeuterhyperol = {10,10[1,1,2\3]2}
terrible backootritohyperol = {10,10[1,1,1,2\3]2}
terrible backoodimensol = {10,10[1[2]2\3]2}
terrible backoobackoogol = {10,10[1[1\2]2\3]2}
dulinserted terrible backoobackoogol = {10,10[1[1\3]2\3]2}
trilinserted terrible backoobackoogol = {10,10[1[1[1\3]2\3]2\3]2}
terrible terrible backoogol = {10,10[1\4]2}
terrible terrible terrible backoogol = {10,10[1\5]2}
backiteroogol / backoohyperigol = {10,10[1\1,2]2}
terrible backiteroogol / terrible backoohyperigol = {10,10[1\2,2]2}
terrible terrible backiteroogol / terrible backoohyperigol = {10,10[1\3,2]2}
backiteroodugol = {10,10[1\1,3]2}
backiterootrigol = {10,10[1\1,4]2}
backiteroohyperigol / backiterhyperoogol = {10,10[1\1,1,2]2}
terrible backiteroohyperigol = {10,10[1\2,1,2]2}
backiteroohyperidugol = {10,10[1\1,2,2]2}
backiterooduhyperigol = {10,10[1\1,1,3]2}
terrible backiterooduhyperigol = {10,10[1\2,1,3]2}
backiterootrihyperigol = {10,10[1\1,1,4]2}
backiterootryperigol = {10,10[1\1,1,1,2]2}
backiterootetryperigol = {10,10[1\1,1,1,1,2]2}
backiteroohyperidugol = {10,10[1\1,2,2]2}
backiterooquadryperigol = {10,10[1\1,1,1,1,2]2}
backiteroodimenperigol / backispatialoogol = {10,10[1\1[2]2]2}
terrible backispatialoogol = {10,10[1\2[2]2]2}
backispatialiteroogol = {10,10[1\1,2[2]2]2}
backispatialiterohyperoogol = {10,10[1\1,1,2[2]2]2}
backispatialtreteroogol = {10,10[1\1[2]3]2}
backispatialquadreteroogol = {10,10[1\1[2]4]2}
backoohyperspatialoogol = {10,10[1\1[2]1,2]2}
backootryperspatialoogol = {10,10[1\1[2]1,1,2]2}
backoodeuterspatialoogol = {10,10[1\1[2]1[2]2]2}
backootritospatialoogol = {10,10[1\1[2]1[2]1[2]2]2}
backigridispatialoogol = {10,10[1\1[3]2]2}
backicubispatialoogol = {10,10[1\1[4]2]2}
backisuperspatialoogol / backoogomgathitergol = {10,10[1\1[1,2]2]2}
backoogomtothitergol = {10,10[1\1[1[2]2]2]2}
backoogomtertitergol = {10,10[1\1[1[1,2]2]2]2}
backoogomtopitergol = {10,10[1\1[1[1[2]2]2]2]2}
dustaculated-backoogol / backoogol-turreted-backoogol = {10,10[1\1[1\2]2]2}
terribackoogol-turreted-backoogol = {10,10[1\1[1\3]2]2}
tristaculated-backoogol = {10,10[1\1[1\1[1\2]2]2]2}
tetrastaculated-backoogol = {10,10[1\1[1\1[1\1[1\2]2]2]2]2}
pentastaculated-backoogol = {10,10[1\1[1\1[1\1[1[1\2]2\2]2]2]2]2}
backoocross = {10,10[1\1\2]2}
Cumulative numbers: 298
(up to 1\1\1\2)
To prevent any mixups between numbers... I will just borrow from Extended Cascading-E naming scheme.
backoocrossplex = {10,3,2[1\1\2]2}
backigcross = {10,10,2[1\1\2]2}
backagcross = {10,10,3[1\1\2]2}
backugolcross = {10,10,10[1\1\2]2}
backootroocross = {10,10,10,10[1\1\2]2}
backoiterabocross = {10,10[2]2[1\1\2]2}
backoogootrocross = {10,10[2]3[1\1\2]2}
backoogooquadrocross = {10,10[2]4[1\1\2]2}
backoogoohyperocross = {10,10[2]1,2[1\1\2]2}
backoogomgathocross = {10,10[1,2]1[1\1\2]2}
backoogomtothocross = {10,10[1[2]2]1[1\1\2]2}
backoogol-carta-backoocross = {10,10[1\2]1[1\1\2]2}
terribackoogol-carta-backoocross = {10,10[1\3]1[1\1\2]2}
territerribackoogol-carta-backoocross = {10,10[1\4]1[1\1\2]2}
backiteroogol-carta-backoocross = {10,10[1\1,2]1[1\1\2]2}
backiterhyperoogol-carta-backoocross = {10,10[1\1,1,2]1[1\1\2]2}
backispatialoogol-carta-backoocross = {10,10[1\1[2]2]1[1\1\2]2}
dustaculbackoogol-carta-backoocross = {10,10[1\1[1\2]2]1[1\1\2]2}
tristaculbackoogol-carta-backoocross = {10,10[1\1[1\1[1\2]2]2]1[1\1\2]2}
backoocross-by-deuteron = {10,10[1\1\2]3}
backoocross-by-triton = {10,10[1\1\2]4}
backoocross-by-hyperon = {10,10[1\1\2]10}
backoocross-by-boogol = {10,10[1\1\2]100}
backoocross-by-A = {10,10[1\1\2]1,2}
backoocross-by-troogol = {10,10[1\1\2]10,100}
backoocross-by-B = {10,10[1\1\2]1,1,2}
backoocross-by-goobol = {10,10[1\1\2]1[2]2}
backoocross-by-gomgathor = {10,10[1\1\2]1[1,2]2}
backoocross-by-backoogol = {10,10[1\1\2]1[1\2]2}
backoocross-by-terribackoogol = {10,10[1\1\2]1[1\3]2}
backoocross-by-territerribackoogol = {10,10[1\1\2]1[1\4]2}
backoocross-by-backiteroogol = {10,10[1\1\2]1[1\1,2]2}
backoocross-by-backiterhyperoogol = {10,10[1\1\2]1[1\1,1,2]2}
backoocross-by-backispatialoogol = {10,10[1\1\2]1[1\1[2]2]2}
backoocross-by-backigridispatialoogol = {10,10[1\1\2]1[1\1[3]2]2}
backoocross-by-backigridispatialoogol = {10,10[1\1\2]1[1\1[3]2]2}
deutero-backoocross = {10,10[1\1\2]1[1\1\2]2}
trito-backoocross = {10,10[1\1\2]1[1\1\2]1[1\1\2]2}
teterto-backoocross = {10,10[1\1\2]1[1\1\2]1[1\1\2]1[1\1\2]2}
backoocruxifact = {10,10[2\1\2]2}
backoocruxifact-by-backoocross = {10,10[2\1\2]1[1\1\2]2}
backoocruxideuterfact = {10,10[3\1\2]2}
backoocruxitritofact = {10,10[4\1\2]2}
backoocruxitetertofact = {10,10[5\1\2]2}
backoocruxipeptofact = {10,10[6\1\2]2}
quadratatebackoocross = {10,10[1,2\1\2]2}
backoocross-ipso-goobol = {10,100[1,2\1\2]2}
backoocross-ipso-gomgathor = {10,10[1[1,2]2\1\2]2}
backoocross-ipso-gomtothol = {10,10[1[1[2]2]2\1\2]2}
backoocross-ipso-backoogol = {10,10[1[1\2]2\1\2]2} (colored to make sure the changes)
backoocross-ipso-deutero-backoogol = {10,10[1[1\2]1[1\2]2\1\2]2}
backoocross-ipso-deutero-backoogol = {10,10[1[1\2]1[1\2]2\1\2]2}
backoocross-ipso-backoogolfact = {10,10[1[2\2]2\1\2]2}
backoocross-ipso-dutetrated-backoogol = {10,10[1[1[1\2]2\2]2\1\2]2}
backoocross-ipso-tritetrated-backoogol = {10,10[1[1[1[1\2]2\2]2\2]2\1\2]2}
backoocross-ipso-terribackoogol = {10,10[1[1\3]2\1\2]2}
backoocross-ipso-territerribackoogol = {10,10[1[1\4]2\1\2]2}
backoocross-ipso-backiteroogol = {10,10[1[1\1,2]2\1\2]2}
backoocross-ipso-terribackiteroogol = {10,10[1[1\2,2]2\1\2]2}
backoocross-ipso-backiteroodugol = {10,10[1[1\1,3]2\1\2]2}
backoocross-ipso-backiterhyperoogol = {10,10[1[1\1,1,2]2\1\2]2}
backoocross-ipso-backispatialoogol = {10,10[1[1\1[2]2]2\1\2]2}
backoocross-ipso-dustaculbackoogol = {10,10[1[1\1[1\2]2]2\1\2]2}
backoocross-ipso-tristaculbackoogol = {10,10[1[1\1[1[1\2]2\2]2]2\1\2]2}
backoocross-ipso-tristaculbackoogol = {10,10[1[1\1[1[1\2]2\2]2]2\1\2]2}
dulinserted-backoocross = {10,10[1[1\1\2]2\1\2]2}
trilinserted-backoocross = {10,10[1[1[1\1\2]2\1\2]2\1\2]2}
terrible backoocross = {10,10[1\2\2]2}
terrible terrible backoocross = {10,10[1\3\2]2}
territerated backoocross = {10,10[1\1,2\2]2}
terrigriditerated backoocross = {10,10[1\1,1,2\2]2}
terricubiterated backoocross = {10,10[1\1,1,1,2\2]2}
terrispatialated backoocross / iteral-turreted-terribackoocross = {10,10[1\1[2]2\2]2}
xappol-turreted-terribackoocross = {10,10[1\1[3]2\2]2}
colossol-turreted-terribackoocross = {10,10[1\1[4]2\2]2}
gomgathor-turreted-terribackoocross = {10,10[1\1[1,2]2\2]2}
gramgathor-turreted-terribackoocross = {10,10[1\1[1,1,2]2\2]2}
gomtothol-turreted-terribackoocross = {10,10[1\1[1[2]2]2\2]2}
backoogol-turreted-terribackoocross = {10,10[1\1[1[1\2]2]2\2]2}
terribackoogol-turreted-terribackoocross = {10,10[1\1[1[1\3]2]2\2]2}
backiteroogol-turreted-terribackoocross = {10,10[1\1[1[1\1,2]2]2\2]2}
dustaculbackoogol-turreted-terribackoocross = {10,10[1\1[1[1\1[1\2]2]2]2\2]2}
backoocross-turreted-terribackoocross = {10,10[1\1[1\1\2]2\2]2}
A steep climb to the next milestone now...
dustaculated-terribackoocross = {10,10[1\1[1\2\2]2\2]2}
tristaculated-terribackoocross = {10,10[1\1[1\1[1\2\2]2\2]2\2]2}
backooducross / terrisquared backoocross = {10,10[1\1\3]2}
backootricross = {10,10[1\1\4]2}
backootetercross = {10,10[1\1\5]2}
backitercross = {10,10[1\1\1,2]2}
backigriditercross = {10,10[1\1\1,1,2]2}
backispatialcross = {10,10[1\1\1[2]2]2}
backoogol-turreted-backoocross = {10,10[1\1\1[1\2]2]2}
dustaculated-backoocross = {10,10[1\1\1[1\1\2]2]2}
tristaculated-backoocross = {10,10[1\1\1[1\1\1[1\1\2]2]2]2}
backoocubor = {10,10[1\1\1\2]2}
Cumulative numbers: 393
Note that I am using the modified Hierarchial Hyper-Nested Array Notation by Douglas Shamlin Jr., in which ~ is replaced by ¬, / replaced by \,
To (2 ¬ 2) (the end of 1-hyperseparator)
To (1\1\1\1\2)
backoocuborplex = {10,3,2[1\1\1\2]2}
backigcubor = {10,10,2[1\1\1\2]2}
backagcubor = {10,10,3[1\1\1\2]2}
backugolcubor = {10,10,10[1\1\1\2]2}
backoocubor-by-deuteron = {10,10[1\1\1\2]3}
backoocubor-by-triton = {10,10[1\1\1\2]4}
backoocubor-by-omega = {10,10[1\1\1\2]1,2}
backoocubor-by-iteral = {10,10[1\1\1\2]1[2]2}
backoocubor-by-xappol = {10,10[1\1\1\2]1[3]2}
backoocubor-by-gomgathor = {10,10[1\1\1\2]1[1,2]2}
backoocubor-by-gomtothol = {10,10[1\1\1\2]1[1[2]2]2}
backoocubor-by-backoogol = {10,10[1\1\1\2]1[1\2]2}
backoocubor-by-backoocross = {10,10[1\1\1\2]1[1\1\2]2}
deutero-backoocubor = {10,10[1\1\1\2]1[1\1\1\2]2}
trito-backoocubor = {10,10[1\1\1\2]1[1\1\1\2]1[1\1\1\2]2}
backoocuborfact = {10,10[2\1\1\2]2}
backoocubordeuterfact = {10,10[3\1\1\2]2}
quadratabackoocubor = {10,10[1[2]2\1\1\2]2}
backoocubor-ipso-xappol = {10,10[1[3]2\1\1\2]2}
backoocubor-ipso-gomgathor = {10,10[1[1,2]2\1\1\2]2}
backoocubor-ipso-backoogol = {10,10[1[1\2]2\1\1\2]2}
backoocubor-ipso-backoocross = {10,10[1[1\1\2]2\1\1\2]2}
dulinserted-backoocubor = {10,10[1[1\1\1\2]2\1\1\2]2}
terrible backoocubor = {10,10[1\2\1\2]2}
territerated backoocubor = {10,10[1\1,2\1\2]2}
iteral-turreted-terribackoocubor = {10,10[1\1[2]2\1\2]2}
backoogol-turreted-terribackoocubor = {10,10[1\1[1\2]2\1\2]2}
backoocross-turreted-terribackoocubor = {10,10[1\1[1\1\2]2\1\2]2}
backoocubor-turreted-terribackoocubor = {10,10[1\1[1\1\1\2]2\1\2]2}
dustaculated-terribackoocubor = {10,10[1\1[1\2\1\2]2\1\2]2}
terrisquared backoocubor = {10,10[1\1\2\2]2}
The Wun and only = {11,11[1\11\2\2]11}
double terrisquared backoocubor = {10,10[1\1\3\2]2}
territersquared backoocubor = {10,10[1\1\1,2\2]2}
iteral-turreted-terrisquared backoocubor = {10,10[1\1\1[2]2\2]2}
backoogol-turreted-terrisquared backoocubor = {10,10[1\1\1[1\2]2\2]2}
backoocross-turreted-terrisquared backoocubor = {10,10[1\1\1[1\1\2]2\2]2}
backoocubor-turreted-terrisquared backoocubor = {10,10[1\1\1[1\1\1\2]2\2]2}
dustaculated-terrisquared backoocubor = {10,10[1\1\1[1\1\2\2]2\2]2}
tristaculated-terrisquared backoocubor = {10,10[1\1\1[1\1\1[1\1\2\2]2\2]2\2]2}
backooducubor = {10,10[1\1\1\3]2}
backootricubor = {10,10[1\1\1\4]2}
backitercubor = {10,10[1\1\1\1,2]2}
backigridicubor = {10,10[1\1\1\1,1,2]2}
backispatialcubor = {10,10[1\1\1\1[2]2]2}
backoogol-turreted-backoocubor = {10,10[1\1\1\1[1\2]2]2}
backoocross-turreted-backoocubor = {10,10[1\1\1\1[1\1\2]2]2}
dustaculated-backoocubor = {10,10[1\1\1\1[1\1\1\2]2]2}
tristaculated-backoocubor = {10,10[1\1\1\1[1\1\1\1[1\1\1\2]2]2]2}
backooteron = {10,10[1\1\1\1\2]2}
Cumulative numbers: 443
To (2 ¬ 2)
backooteronifact = {10,10[2\1\1\1\2]2}
terrible backooteron = {10,10[1\2\1\1\2]2}
terrisquared backooteron = {10,10[1\1\2\1\2]2}
terricubed backooteron = {10,10[1\1\1\2\2]2}
backooduteron = {10,10[1\1\1\1\3]2}
backootriteron = {10,10[1\1\1\1\4]2}
backiterteron = {10,10[1\1\1\1\1,2]2}
backispatialteron = {10,10[1\1\1\1\1[2]2]2}
dustaculated-backooteron = {10,10[1\1\1\1\1[1\1\1\1\2]2]2}
backoopeton = {10,10[1\1\1\1\1\2]2}
backiterpeton = {10,10[1\1\1\1\1\1,2]2}
backoohexon = {10,10[1\1\1\1\1\1\2]2}
backoohepton = {10,10[1\1\1\1\1\1\1\2]2}
backoo-ogdon / backoo-octon = {10,10[1\1\1\1\1\1\1\1\2]2}
backootope = {10,10[1[2¬2]2]2}
Cumulative numbers: 458
To the end?
To Gamma zero
backootopeplex = {10,3,2[1[2¬2]2]2}
backigtope = {10,10,2[1[2¬2]2]2}
backagtope = {10,10,3[1[2¬2]2]2}
backugtope = {10,10,10[1[2¬2]2]2}
backiteralotope = {10,10[2]2[1[2¬2]2]2}
backootope-by-deuteron = {10,10[1[2¬2]2]3}
deutero-backootope = {10,10[1[2¬2]2]1[1[2¬2]2]2}
trito-backootope = {10,10[1[2¬2]2]1[1[2¬2]2]1[1[2¬2]2]2}
backootopofact = {10,10[2[2¬2]2]2}
backootopodeuterfact = {10,10[3[2¬2]2]2}
quadratabackootope = {10,10[1,2[2¬2]2]2}
kubikubackootope = {10,10[1,1,2[2¬2]2]2}
backootope-ipso-iteral = {10,10[1[2]2[2¬2]2]2}
backootope-ipso-xappol = {10,10[1[3]2[2¬2]2]2}
backootope-ipso-gomgathor = {10,10[1[1,2]2[2¬2]2]2}
backootope-ipso-gomtothol = {10,10[1[1[2]2]2[2¬2]2]2}
backootope-ipso-backoogol = {10,10[1[1\2]2[2¬2]2]2}
backootope-ipso-backoocross = {10,10[1[1\1\2]2[2¬2]2]2}
dulinserted-backootope = {10,10[1[1[2¬2]2]2[2¬2]2]2}
terrible backootope = {10,10[1\2[2¬2]2]2}
terrisquared backootope = {10,10[1\1\2[2¬2]2]2}
terricubed backootope = {10,10[1\1\1\2[2¬2]2]2}
backoodutope = {10,10[1[2¬2]3]2}
backootritope = {10,10[1[2¬2]4]2}
backitertope = {10,10[1[2¬2]1,2]2}
backispatialtope = {10,10[1[2¬2]1[2]2]2}
backoogol-turreted-backootope = {10,10[1[2¬2]1[1\2]2]2}
backoocross-turreted-backootope = {10,10[1[2¬2]1[1\1\2]2]2}
backoocubor-turreted-backootope = {10,10[1[2¬2]1[1\1\1\2]2]2}
dustaculated-backootope = {10,10[1[2¬2]1[1[2¬2]2]2]2}
tristaculated-backootope = {10,10[1[2¬2]1[1[2¬2]1[1[2¬2]2]2]2]2}
backootopothoth = {10,10[1[2¬2]1\2]2}
backootopocross = {10,10[1[2¬2]1\1\2]2}
backootopocubor = {10,10[1[2¬2]1\1\1\2]2}
backootopodeus = {10,10[1[2¬2]1[2¬2]2]2}
backootopotruce = {10,10[1[2¬2]1[2¬2]1[2¬2]2]2}
backoolattitope = {10,10[1[3¬2]2]2}
backoocubitope = {10,10[1[4¬2]2]2}
backooquarticutope = {10,10[1[5¬2]2]2}
backulto-hyperope = {10,10[1[1,2¬2]2]2}
backulto-deuterhyperope = {10,10[1[1,1,2¬2]2]2}
backulto-trithyperope = {10,10[1[1,1,1,2¬2]2]2}
backulto-iteralope = {10,10[1[1[2]2¬2]2]2}
backulto-gomgathope = {10,10[1[1[1,2]2¬2]2]2}
backulto-gomtothope = {10,10[1[1[1[2]2]2¬2]2]2}
backulto-backoogolope / backarxitri = {10,10[1[1[1\2]2¬2]2]2}
backulto-backoocrossope = {10,10[1[1[1\1\2]2¬2]2]2}
backulto-backoocuborope = {10,10[1[1[1\1\1\2]2¬2]2]2}
backulto-backootopotope = {10,10[1[1[1[2¬2]2]2¬2]2]2}
backulto-backoolattitopotope = {10,10[1[1[1[3¬2]2]2¬2]2]2}
dubackulto-hypertope = {10,10[1[1[1[1,2¬2]2]2¬2]2]2}
dubackulto-iteralope = {10,10[1[1[1[1[2]2¬2]2]2¬2]2]2}
backarxitet = {10,10[1[1[1[1[1\2]2¬2]2]2¬2]2]2}
backarxipent = {10,5[1[1\2¬2]2]2}
pentabackthulhum = {10,10[1[1\2¬2]2]2}
Cumulative numbers: 513
To Ackermann ordinal (phi(1,0,0,0) in Extended Veblen function)
pentabackthulhumplex = {10,3,2[1[1\2¬2]2]2}
pentabackthulhufact = {10,10[2[1\2¬2]2]2}
quadratapentabackthulhum = {10,10[1,2[1\2¬2]2]2}
kubikupentabackthulhum = {10,10[1,1,2[1\2¬2]2]2}
terrible pentabackthulhum = {10,10[1\2[1\2¬2]2]2}
terrisquared pentabackthulhum = {10,10[1\1\2[1\2¬2]2]2}
terricubed pentabackthulhum = {10,10[1\1\1\2[1\2¬2]2]2}
territoped pentabackthulhum = {10,10[1[2¬2]2[1\2¬2]2]2}
terrilattitoped pentabackthulhum = {10,10[1[3¬2]2[1\2¬2]2]2}
hyper-tetrated-pentabackthulhum = {10,10[1[1,2¬2]2[1\2¬2]2]2}
iteral-tetrated-pentabackthulhum = {10,10[1[1[2]2¬2]2[1\2¬2]2]2}
backoogol-tetrated-pentabackthulhum = {10,10[1[1[1\2]2¬2]2[1\2¬2]2]2}
backootope-tetrated-pentabackthulhum = {10,10[1[1[1[2¬2]2]2¬2]2[1\2¬2]2]2}
backarxitri-tetrated-pentabackthulhum = {10,10[1[1[1[1[1\2]¬2]2]2¬2]2[1\2¬2]2]2}
dupentated-pentabackthulhum = {10,10[1[1[1[1\2¬2]2]2¬2]2[1\2¬2]2]2}
tripentated-pentabackthulhum = {10,10[1[1[1[1[1[1\2¬2]2]2¬2]2[1\2¬2]2]2¬2]2[1\2¬2]2}2}
pentabackthuldeucthulhum / horrible pentabackhthulhum = {10,10[1[1\2¬2]3]2}
pentabackthultricthulhum / horrible horrible pentabackhthulhum = {10,10[1[1\2¬2]4]2}
pentabackthuliterate = {10,10[1[1\2¬2]1,2]2}
pentabackthulspatialate = {10,10[1[1\2¬2]1[2]2]2}
backoogol-turreted-pentabackthulhum = {10,10[1[1\2¬2]1[1\2]2]2}
backootope-turreted-pentabackthulhum = {10,10[1[1\2¬2]1[1[2¬2]2]2}
dustaculated-pentabackthulhum = {10,10[1[1\2¬2]1[1[1\2¬2]2]2}
pentabackthulcross = {10,10[1[1\2¬2]1\2]2}
horrible pentabackthulcross = {10,10[1[1\2¬2]2\2]2}
horriterated pentabackthulcross = {10,10[1[1\2¬2]1,2\2]2}
dustaculated horripentabackthulcross = {10,10[1[1\2¬2]1[1[1\2¬2]2\2]2\2]2}
pentabackthulducross = {10,10[1[1\2¬2]1\3]2}
pentabackthulitercross = {10,10[1[1\2¬2]1\1,2]2}
dustaculated-pentabackthulcross = {10,10[1[1\2¬2]1\1[1[1\2¬2]1\2]2]2}
pentabackthulcubor = {10,10[1[1\2¬2]1\1\2]2}
pentabackthulteron = {10,10[1[1\2¬2]1\1\1\2]2}
pentabackthultope = {10,10[1[1\2¬2]1[2¬2]2]2}
pentabackthuldutope = {10,10[1[1\2¬2]1[2¬2]3]2}
pentabackthultopothoth = {10,10[1[1\2¬2]1[2¬2]1\2]2}
pentabackthultopodeus = {10,10[1[1\2¬2]1[2¬2]1[2¬2]2]2}
pentabackthulattitope = {10,10[1[1\2¬2]1[3¬2]2]2}
pentabackthulcubitope = {10,10[1[1\2¬2]1[4¬2]2]2}
pentabackthulto-hyperope = {10,10[1[1\2¬2]1[1,2¬2]2]2}
pentabackthulto-iteralope = {10,10[1[1\2¬2]1[1[2]2¬2]2]2}
pentabackthulto-backoogolope = {10,10[1[1\2¬2]1[1[1\2]2¬2]2]2}
pentabackthulto-backoocrossope = {10,10[1[1\2¬2]1[1[1\1\2]2¬2]2]2}
pentabackthulto-backootopope = {10,10[1[1\2¬2]1[1[1[2¬2]2]2¬2]2]2}
pentabackthularxitri = {10,10[1[1\2¬2]1[1[1[1\2¬2]2]2¬2]2]2}
hexabackthulhum = {10,10[1[1\2¬2]1[1\2¬2]2]2}
hexabackthulcross = {10,10[1[1\2¬2]1[1\2¬2]1\2]2}
heptabackthulhum = {10,10[1[1\2¬2]1[1\2¬2]1[1\2¬2]2]2}
octabackthulhum = {10,10[1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]2]2}
backongulus = {10,10[1[2\2¬2]2]2}
backongulhen = {10,10[1[2\2¬2]1[1\2¬2]2]2}
backonguldeus = {10,10[1[2\2¬2]1[2\2¬2]2]2}
backongridgus = {10,10[1[3\2¬2]2]2}
backonkubikus = {10,10[1[4\2¬2]2]2}
backonhyperus = {10,10[1[1,2\2¬2]2]2}
blasphemorbackulus = {10,10[1[1\3¬2]2]2}
Cumulative numbers: 568
To the limit....
super blasphemorbackulus = {10,10[1[2\3¬2]2]2}
mega blasphemorbackulus = {10,10[1[1\4¬2]2]2}
giga blasphemorbackulus = {10,10[1[1\5¬2]2]2}
small veblasphemorbackulus = {10,10[1[1\1,2¬2]2]2} (comparable to Small Veblen Ordinal, as the name suggests)
backoogol-veblasphemorbackulus = {10,10[1[1\1[1 \ 2]2¬2]2]2}
large veblasphemorbackulus = {10,10[1[1\1\2¬2]2]2} (comparable to Large Veblen Ordinal, as the name suggests)
trilarge veblasphemorbackulus = {10,10[1[1\1\2¬2]1[1\2¬2]2]2}
expanded large veblasphemorbackulus = {10,10[1[1\1\2¬2]1[1\3¬2]2]2}
largeyper veblasphemorbackulus = {10,10[1[2\1\2¬2]2]2}
xappling large veblasphemorbackulus = {10,10[1[1\1\1,2¬2]2]2}
mega veblasphemorbackulus = {10,10[1[1\1\1\2¬2]2]2}
dual tetrated veblasphemorbackulus = {10,10[1[1[1\2¬2]2¬2]2]2} (comparable to ψ_0(Ω^^4) in fast-growing hierarchy, using the FS of Extended Buchholz's OCF)
triple tetrated veblasphemorbackulus = {10,10[1[1[1\1\2¬2]2¬2]2]2} (comparable to ψ_0(Ω^^5) in fast-growing hierarchy, using the FS of Extended Buchholz's OCF)
quadruple tetrated veblasphemorbackulus = {10,10[1[1[1[1\2¬2]2¬2]2¬2]2]2} (comparable to ψ_0(Ω^^6) in fast-growing hierarchy, using the FS of Extended Buchholz's OCF)
bachobackulus = {10,10[1[1¬3]2]2} (comparable to Bachmann-Howard ordinal, as the name suggests)
The inutero of Nests = {10,16[1[1¬3]2[1¬3]2]2}
dubachobackulus = {10,10[1[1¬4]2]2}
bachohyperbackulus = {10,10[1[1¬1,2]2]2}
bacho-slash-backulus = {10,10[1[1¬1\2]2]2}
bacho-slash-dubackulus = {10,10[1[1¬1\3]2]2}
bacho-duslash-backulus = {10,10[1[1¬1\1\2]2]2}
bacho-topo-backulus = {10,10[1[1¬1[2¬2]2]2]2}
array backulus = {10,10[1[1¬1¬2]2]2}
s array backulus = {10,10[1[1¬1¬1\2]2]2}
array backulus 2 = {10,10[1[1¬1¬1¬2]2]2}
array backulus 3 = {10,10[1[1¬1¬1¬1¬2]2]2}
striking backulus = {10,10[1[1[2 \3 2]2]2}
more striking backulus = {10,10[1[1[1[1\2]2 \3 2]2]2]2}
bachostriking backulus = {10,10[1[1[1\2 \3 2]2]2]2}
double---backulus = {10,10[1[1[1¬2 \3 2]2]2]2}
duper backulus = {10,10[1[1[1[2 \4 2]2]2]2}
truper backulus = {10,10[1[1[1[1 [2 \5 2] 2]2]2]2}
new ones = {10,10[1[2 \1,2 2]2]2}
The TFB backulus = {10,10[1[1[1 \2,2 3]2]2]2} (comparable to ψ_0(ε_(Ω_ω+1)) (TFB ordinal) in fast-growing hierarchy, using the FS of Extended Buchholz's OCF)
(to be named) = {10,10[1[2 \1,1,2 2]2]2}
(to be named 2) = {10,10[1[2 \1[2]2 2]2]2}
(to be named 3) = {10,10[1[2 \1[1\2]2 2]2]2}
New numbers (name TBC) = {10,10[1[2 \1(1\2)2 2]2]2}
Omega backulus = {10,10[1[2 \(1\2) 2]2]2}
Gated omega backulus = {10,10[1[1,2 \(1\2) 2]2]2}
Next omega backulus = {10,10[1[2 \(1\3) 2]2]2}
More omega backulus = {10,10[1[2 \(1\1\2) 2]2]2}
Total so far: 610 (but I will expand more after done with Extended Hyper-E)
Finishing Bird's array notation for now... but obviously will be expanded later.