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This works as expected:

Table[x[1], {x[1], 1, 10}]

However, the parallel version

ParallelTable[x[1], {x[1], 1, 10}]

complains that the expression cannot be parallelized. (The same applies to other iterators like Subscript[x,1] etc. instead of x[1].) How can I fix that?

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This works as well, similar to Sjoerd C. de Vries' method:

Block[{x}, x[1] = Unique[]; ParallelTable[x[1], {x[1], 1, 10}]]

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

And this does, too:

Block[{x}, x /: Subscript[x, i] = Unique[]; 
 ParallelTable[Subscript[x, i], {Subscript[x, i], 1, 10}]]

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

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This works, but looks rather clumsy to me:

Hold[ParallelTable[x[1], {x[1], 1, 10}]] /.  x[i_] -> Unique[] // ReleaseHold

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Also works for subscripts:

Hold[ParallelTable[Subscript[x, i], {Subscript[x, i], 1, 10}]] /. 
     Subscript[x, i_] -> Unique[] // ReleaseHold

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

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