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Perl 6, 25 characters

{grep({$_-.Num},^∞)[^$_]}

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This is 27 bytes, but the challenge is scored in characters.

This should work theoretically. This creates a lazy list of numbers that compares the default number type (with arbitrary precision) against the same number converted to a Num datatype, which is a 64-bit floating point number, and returns the first \$n\$ elements of the list.