The Bouncer of the Last Circle

Question

Following the success of your last paper, you received an invitation to The Last Circle, a private bar for mathematicians and logicians. But the bouncer in front of the only entrance won't let you in no matter what. After observing (and listening to) some others going into the bar, you've learned that:

1 = 7
6 = 7
8 = 7
9 = 7
10 = 7
1,000,000 = 7

So, to no surprise, you are about to come up to the bouncer and answer with lucky number 7, but two more clients arrive and, this time, the answers are different:

20 = 8
30 = 12

You sit down on a nearby bench, confused, but after a bit of thinking, you come up to the bouncer. He simply says, in a deep voice: "18"

What do you need to answer to gain access to the bar ?

Hints:

2 and 4 do not lead to an answer of 7

Begon, weird shapes !

Answer 1

You should answer:

11

Because:

The answer for N is the number of letters in the name of an N-sided polygon.
1 - monogon - 7
6 - hexagon - 7
8 - octagon - 7
9 - nonagon - 7
10 - decagon - 7
1000000 - megagon - 7

20 - icosagon - 8
30 - triacontagon - 12

So we have 18 - octadecagon - 11 letters