Hyper-B Notation

Hyper-B Notation is a notation created by Googology Wiki user BlankEntity.BlankEntity's Googology - Hyper-B Notation (retrieved 13 June 2022) Unfortunately, it is ill-defined by the reason explained in the #Issues section and the creator clarified in the talk page that it might be fixed with the statement "I might make one last attempt at fixing this notation, but don't count on it.".
== Definition ==
=== LAN ===
@ is a part of the array or the rest of the array
If there is 2 entries:
B(a) = a
B(a,b) = a^b
Otherwise, start the process below:
*Scan the array:
*If you find an entry that is 1, then:
** If it is the last entry, remove it from the array (Example: B(5,3,1) = B(5,3)) else:
** Keep advancing through the array until there is a non-one entry, then turn the 1 entry into the non-one entry and reduce the non-one entry by 1
** If there is no non-one entries, then the result is 1
*Otherwise, B(a,b,c@) = B(a,b-1@,B(a,b,c-1@))
=== Separators ===
% is a part of the array or the rest of the array
I define my notation B(@{1}%) in the following recursive way:
B(a{1}%) = a
B(a,b{1}2) = B(a,b,b,...,b,b) with b entries
B(a,b{1}%) = B(a,b,b,...{1}%,k-1) where k is the last entry in %.
B(a,b,c{1}2) = B(a,b-1,B(a,b,c-1){1}2)
B(a,b,c@{1}n) = B(a,b-1@,B(a,b,c-1@){1}n)
B(a,b,c@{1}n,m) = B(a,b-1@,B(a,b,c-1@){1}B(B(a,b-1@,B(a,b,c-1@){1}...B(a,b-1@,B(a,b,c-1@){1}B(B(a,b-1@,B(a,b,c-1@){1}m))...‌)))) with n recursions
B(a,b,c@{1}%) = B(a,b-1@,B(a,b,c-1@){1}%,B(B(a,b-1@,B(a,b,c-1@){1}%,...B(a,b-1@,B(a,b,c-1@){1}%,B(B(a,b-1@,B(a,b,c-1@){1}%))...)))) with k recursions, where k is the last entry in %.
If there is a 1 in the array, use the same process as LAN.
== Issues ==
The Hyper-B notation is ill-defined because the definition on recursion rule is B(a,b,c@) = B(a,b-1@,B(a,b,c-1@)), which may include some ambiguity.
== Sources ==
Category:Notations
Category:Functions
Category:Incomplete