Kata

Introduction

Consider the first 16 terms of the series below:

11,32,53,94,135,176,217,298,379,460,541,622,703,784,865,1026...

which is generated by this sequence:

11,21,21,41,41,41,41,81,81,81,81,81,81,81,81,161....

Each term u of the sequence is obtained by finding the:

(last power of 2) * 10 + 1 if u is not a power of 2.

oru * 10 + 1 if u is a power of 2.

Please note that u starts at 1 and not 0.

Task

Given variable n, calculate the nth term of the series shown above.

Tests

• 10 fixed tests: First 10 terms
• 100 random tests: 1e100 < n < 1e101

Notes:

• Naive solutions won't pass, so don't try to generate the sequence.
• Aim for a sublinear solution (constant time is possible but not required).