Knuth up arrow notation for hyper exponentiation is such an operator.
Ken's paper cited by Roger predates this notation by 10 years.

> Date: Sat, 31 Jul 2010 11:21:57 -0400
> From: "Dan Bron" <[email protected]>
> Subject: [Jprogramming] Order of operations
> To: "'Programming forum'" <[email protected]>
> Message-ID: <013401cb30c4$1d5df050$5819d0...@us>
> Content-Type: text/plain;       charset="us-ascii"
> 
> How did the current mathematical order of operations (PEMDAS) arise?  
> 
> ...introduce a new operator in the chain + * ^, would it necessarily
> also have the highest precedence?


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