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Grangoldex is equal to E100#100#2 = E100#(E100#100) = EE...EE100 (grangol E's) = 101010...1010100 (grangol 10's), using Hyper-E Notation.[1] The term was coined by Sbiis Saibian.

## Contents

### Etymology

The name of the number is based on suffix -dex and the number grangol.

### Approximations in other notations

Notation Lower bound Upper bound
Arrow notation $$57 \uparrow\uparrow (57 \uparrow\uparrow 101)$$ $$58 \uparrow\uparrow (58 \uparrow\uparrow 101)$$
Chained arrow notation $$57 \rightarrow (57 \rightarrow 101 \rightarrow 2) \rightarrow 2$$ $$58 \rightarrow (58 \rightarrow 101 \rightarrow 2) \rightarrow 2$$
BEAF {57,{57,101,2},2} {58,{58,101,2},2}
Bird's array notation {57,{57,101,2},2} {58,{58,101,2},2}
Hyperfactorial array notation $$(102!1)!1$$ $$(103!1)!1$$
Fast-growing hierarchy $$f_3(f_3(100))$$ $$f_3(f_3(101))$$
Hardy hierarchy $$H_{(\omega^3) 2}(100)$$ $$H_{(\omega^3) 2}(101)$$
Slow-growing hierarchy $$g_{\varepsilon_{\varepsilon_0}}(100)$$ $$g_{\varepsilon_{\varepsilon_0}}(101)$$

### Sources

1. Saibian, Sbiis. Hyper-E Numbers. Retrieved 2015-03-01.