BOX M̃

BOX_M̃ is a large number coined by Marco Ripà.


 * \(n\$ = {}^{n!}(n!)\) (Clifford Pickover's superfactorial)
 * \(n¥ = {}^{n!}(n\$) \uparrow \cdots \uparrow {}^{2!}(2\$) \uparrow {}^{1!}(1\$)\)
 * \(n\widetilde{¥} = {}^{n\$}(n\$) \uparrow \cdots \uparrow {}^{2\$}(2\$) \uparrow {}^{1\$}(1\$)\)
 * \(n£ = {}^{n\widetilde{¥}}(n\widetilde{¥}) \uparrow \cdots \uparrow {}^{2\widetilde{¥}}(2\widetilde{¥}) \uparrow {}^{1\widetilde{¥}}(1\widetilde{¥})\)
 * \(A_1 = n£\), \(A_{k + 1} = (A_k)^{(A_k)}\)
 * \(M_1(a) = a \uparrow^{a} a\), \(M_{k + 1}(a) = a \uparrow^{M_k(a)} a\)
 * \(k_1 = M_{n£}(A_{n£})!\), \(k_{i + 1} = n \uparrow^{k_i} n\)
 * Set \(n = 2\).
 * \(\widetilde{R} = k_{k_{._{._{._{G£}}}}}\), where \(G\) is Graham's number, and with \(G£\) copies of \(k\)
 * \(\widetilde{M}_1 = (G£ \uparrow^{\widetilde{R}} G£) \rightarrow (G£ \uparrow^{\widetilde{R}} G£) \rightarrow \cdots \rightarrow (G£ \uparrow^{\widetilde{R}} G£) \rightarrow (G£ \uparrow^{\widetilde{R}} G£)\), with \(G£ \uparrow^{\widetilde{R}} G£\) copies
 * \(\widetilde{M}_{k + 1} = \widetilde{M}_k \rightarrow \widetilde{M}_k \rightarrow \cdots \rightarrow \widetilde{M}_k \rightarrow \widetilde{M}_k\), with \(\widetilde{M}_k\) copies
 * \(BOX\_\widetilde{M} = \widetilde{M}_{\widetilde{M}_1 + 1}\)