Decimal places patterns

Recursive function to compute patterns of decimal places when denominator is a repetition of 1 or more '3' and that the numerator is not divisible by the denominator. The decimal places "pattern" has as much digits than the denominator and repeats itself many times. I can't prove it yet but hopefully someone has already found this fun math puzzle

APP_NUMERATOR=475 /usr/bin/php8.0 index.php

You can choose the numerator you like. It must be a positive integer and it must not be divisible by 3

Here the screenshot of the result:

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