Let $n$ a positive integer. I have the following quantity:
$$Q = 3205 \cdot 3^{i-1} + 64i + 64i(3^{i-1}-1)-64(3^{i-1}-1)-32\times3^{i-1}(2i-5)+3$$
I would like to find the integer $i$ which minimizes $Q$, such that $Q \geq n-1$.
Can we give a formula for such $i$ in function of $n$? Is it computable?
Thank you in advance.
Well first thing I put your formula in WA and got that. Sorry for the tinyurl link but WA links are not great because of the parenthesis. Also I replaced $i$ with $k$ to not confuse Him. Assuming I didn't make typo and He is right we have : $$ 3301\cdot3^{k-1}+67 \geq n-1 \\ 3^{k-1} \geq \frac{n-68}{3301} \\ (k-1)log(3) \geq log(n-68) -log(3301) \\ k \geq \frac{log(n-68) -log(3301)}{log(3)} + 1 $$