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Charcoal, 9 bytes
≔¹ξW¹«ξR⁰
Try It Online! Link is to verbose version of code.
Explanation:
≔¹ξ
Assign 1 to X
W¹«
Start The Infinite Loop
ξ
Print X without Casting
R⁰
Refresh with min 0 secs
[Implicit increment]
Every number splits by
[2J[0;0H
I think the The output with trailing separator...