a^^b (a to the hyper-4 power b) is the right associative power tower a^a^...^a^a of height b.
a^^^b (a to the hyper-5 power b) is the right associative hyper-4 power tower a^^a^^...^^a^^a of height b. a^^^-1 = 0, a^^^0 = 1;
We exclude b=1 because otherwise all natural numbers would be in the sequence.
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