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Does BASIC allow padded string formatting? If so, you only need the one loop.
No, but there are other tricks, such as prepending enough zeros and then taking the rightmost 4 characters from the string...

FOR I = 0 TO 9999 : A$ = RIGHT$("000"+STR$(I),4) : ... rest of the code : NEXT I

I saw this headline and pictured him as a hobbit terminator, with BASIC code scrolling down one side of his field of view.