Let's assume we have an A-minor which begins at A1 (I mean 1st octave). According to the interval pattern of minor scale pitches which are in the scale are: A1, B1, C1, D1, E1, F1, G1. Okay, but can I continue the pattern and use A2, B2, C2, etc as pitches of A1-minor?
Your example is in fact A natural minor. There are other minor scales with slightly different notes - but still called 'A minor'.
It matters not which notes you play - they are all actually the white keys on a piano - any (all) of them belong to A minor. You may have trouble singing a song with A4, B7 and C3 - those are big jumps in pitch!
If you start at the lowest white key and play every white key in turn, you have played a seven-and-a-bit octave A natural minor scale, ascending. Most people would play a two or three octave scale, starting somewhere near the middle , say A3 or A4.