The giggoltreunex is equal to s(10,giggolduunex) = s(10,103,2) using strong array notation, or \(10\uparrow\uparrow103\). The term was coined by Aarex Tiaokhiao. Username5243 calls this number Doogoltriunex, and it's equal to 10[1]doogolduunex in Username5243's Array Notation.
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