I found a strange number pattern in Base 10. Does anyone know what it means?

Question

I was trying to think of a good equation for texture smoothing to be used in programming. I came up with this. With texture smoothing however it must be based on division.
$01$ to $10$ = $9$ or $3^2$
$02$ to $20$ = $18$ or $2\times 3^2$
$03$ to $30$ = $27$ or $3^3$
$04$ to $40$ = $36$ or $4\times 3^2$
$05$ to $50$ = $45$ or $5\times 3^2$
$06$ to $60$ = $54$ or $2\times 3^3$
$07$ to $70$ = $63$ or $7\times 3^2$
$08$ to $80$ = $72$ or $8\times 3^2$
$09$ to $90$ = $81$ or $3^4$
Same with 12 to 21, 13 to 31, 14 to 41, 15 to 51, 16, to 61 and so on 243 is $3^5$

Could it be applied to finding prime numbers if I were to elaborate?

Answer 1

Your first pattern follows from $$ 10n - n = 9n. $$

The second follows from

$$ (10n + 1) - (10 + n) = 9n - 9 = 9(n-1). $$

Answer 2

So what you have observed is that for $k\in\{1,2,3,4,5,6,7,8,9\}$: $10k-k=k*3^2$? That's pretty obvious.

No, that can't be applied to finding primes.