MyWiki:Reference desk/Archives/Mathematics/2017 May 31

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May 31

Terminology for a given base raised to a special kind of exponent?

I'm thinking of numbers expressed in a form such as B^(B^(B^(B^(B^X)))), where the chain of 'B' can be of any arbitrary length (eg: 2^(2^(2^3)) = 2^256). Is there a certain term for that sort of representation? Also, interesting links to any known properties would be appreciated as well. Earl of Arundel (talk) 08:24, 31 May 2017 (UTC)

Ah, found this article on symmetric level index arithmetic, which is basically a special case of this (but where B is always equal to Euler's number). Should be a good starting point... Earl of Arundel (talk) 08:35, 31 May 2017 (UTC)

Iterated exponentials (see chart). Loraof (talk) 14:51, 31 May 2017 (UTC)