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Expandotetration refers to the function \(a \{\{4\}\} b = \{a,b,4,2\} = \underbrace{a \{\{3\}\} a \{\{3\}\} \ldots \{\{3\}\} a \{\{3\}\} a}_{b \text{ a's}}\), using BEAF.[1]

In the fast-growing hierarchy, \(f_{\omega+4}(n)\) corresponds to expandotetrational growth rate.

PseudocodeEdit

Below is an example of pseudocode for expandotetration.

function expandotetration(a, b):
    return hyperexpansion(a, b, 4)

function hyperexpansion(a, b, n):
    result := a
    repeat b - 1 times:
        if n = 1:
            result := hyper(a,a,result+2)
        else:
            result := hyperexpansion(a, result, n - 1)
    return result
function hyper(a, b, n):
    if n = 1:
        return a + b
    result := a
    repeat b - 1 times:
        result := hyper(a, result, n - 1)
    return result

Sources Edit

  1. Array Notation by Jonathan Bowers

See also Edit

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