Radical IQ challenge

Question

_{This puzzle is part of the Monthly Topic Challenge #2: IQ Puzzle Parody}

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Can you find out the next one in the sequence, how it's different to the ones before it, and explain the pattern?

1
10
11
20
31
52
121
200
314
512
851
1228

Answer 1

First, take

The powers of 2, from 2⁰ to 2¹⁰:

1, 2, 4, 8, 16, ..., 2048

And now

Based on its position, convert it into that number base. So for instance the second position is now in binary, the third in ternary, etc.

This gives:

1 Base 1 = 1
2 Base 2 = 10
4 Base 3 = 11
8 Base 4 = 20
16 Base 5 = 31
.
.
.
2048 Base 12 = 1228

So the next number is:

4096 Base 13 = 1B31

This differs to the rest as it is the first in the sequence containing a letter!