Question

I’d like to generate definitions of variables using an algorithm.

For example:

i’d like to run a loop that does the following
p=p1
p^2=p2
p^3=p3

so for p^i i’d like to define a variable pi (i is a number).

Answer 1

badListEmulation[varName_?StringQ, maxIndex_?IntegerQ] := 

      ToExpression /@ 
             Table[(varName <> # <> "=" <> varName <> "^" <> #) & [ToString@i], 
                   {i, maxIndex}
             ];

Usage

 badListEmulation["var", 10]

Result

 {var, var^2, var^3, var^4, var^5, var^6, var^7, var^8, var^9, var^10}

 ?var3
 var3=var^3 ... etc

NB:

Of course is MUCH better to use a list. Something like

aList = Table[p^i,{i,6}];

aList[[3]]
p^3

But I guess you already know it.

HTH!