Hyperoperations

H_{n} (a, b) = a [n] b = ⎩ ⎨ ⎧ b + 1 a 01 H_{n - 1} (a, H_{n} (a, b - 1)) n = 0 n = 1 \land b = 0 n = 2 \land b = 0 n \geq 3 \land b = 0 otherwise

$n = 0, 1, 2, 3, 4 \dots$ corresponds to secession, addition, multiplication, exponentiation, tetration, and beyond
E.g.: $H_{4} (2, 4) = 2 [4] 4 = 2 ↑↑ 4 = 2^{2^{2^{2}}}$

Knowledge