Good question. I usually specify which base I'm working in when posting simple arithmetic since someone will invariably ask "what base is that?"

I wonder if employing continuous rather than integer variables, i.e., use fractional base and a fractional number of digits would allow for such a formula.

Then again a large, custom base that used non-tradition orders of symbols could achieve this result rather easily, such as this version of base 36: 0,1,3,5,7,9,2,4,6,8,A,B,C,D...Z, where 1 + 1 = 3, 1 + 3 = 5, and 1 + Z = 10.

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