Weak-b notation

Weak-b notation is a notation created by Wikia user BlankEntityBlankEntity's Googology (Retrieved 21 April, 2022).
== Definition ==
# is a part of the array or the rest of the array
@ is a sequence of 1's separated by commas (or can be empty)
Rules:
b[a] = a
b[a,b] = a+b
Otherwise,
If b[a,b#] = b[a#,@,k], then turn the entry that is 1 into a + k and remove k from the array
If this doesn't apply, then:
b[1,b,c#] = b[b,c#]
b[a,b,c#] = b[a-1,b#,b[a,b-1,c#]]
== Examples ==
b[2,2,2] = b[1,2,b[2,1,2]] = b[1,2,b[2,4]] = b[1,2,6] = b[2,6] = 8
b[3,3,3] = b[2,3,b[3,2,3]] = b[2,3,b[2,2,b[3,1,3]]] = b[2,3,b[2,2,b[3,6]]] = b[2,3,b[2,2,9]] = b[2,3,b[1,2,b[2,1,9]]] = b[2,3,b[1,2,b[2,11]]] = b[2,3,b[1,2,13]] = b[2,3,b[2,13]] = b[2,3,15] = b[1,3,b[2,2,15]] = b[1,3,b[1,2,b[2,1,15]]] = b[1,3,b[1,2,b[2,15]]] = b[1,3,b[1,2,17]] = b[1,3,b[2,17]] = b[1,3,19] = b[3,19] = 22
== Sources ==
Category:Notations