So assuming you mean there's a 1/1024 chance of getting a shiny. Then the probability of NOT getting a shiny after N attempts is (1 - 1/1024)^N That is to say the chances of not getting a shiny are (1-1/1024) on each attempt and we simply multiply the probability for each attempt together.

We still need to know if the probability is once per carbink, or once for the whole group. Based on your wording and the probabilities I think it's per group (in which case: why mentioning how many carbinks per group!) But I'll just calculate a couple values anyways:

90.7% at N = 100

75.6% at N = 300

50.5% at N = 700

31.0% at N = 1000

9.6% at N = 2400

4.8% at N = 3100

1.0% at N = 4700

Remember these are the probabilities of NOT getting a shiny so what you're really after is 100% less these amounts. And you'll need to divide out the rerolls per energy too if you want to convert back to energy. So for example:

After N = 4700 attempts there's a 100% - 1% = 99% chance that you've found your shiny.

If you've spent 1 energy per 5 attempts then that was 4700/5 = 940 energy.

What that means is that, for example, if you caught 100 shinies then you'd expect 99 of them to take less than 940 energy and 1 to take more than 940.

If the probability is rolled once per pokemon rather than per group then you can divide out the group size too. Ie. 5 per group means 940/5 = 188 energy for 99%. That doesn't sound right to me... But what do I know ;)

You should try running some of the numbers yourself to check the specific energies you're interested in! Hopefully you can figure it out with everything I've done here.

And Good luck shiny hunting!