Number sequence quiz

Thread Games
1

Below are two number sequences. Either give the next few numbers or the rule they were generated from. The two sequences are related, so if you get one, you’ll likely get the other. Ideally, you’ll spoiler your answer so you don’t ruin it for others.

0, 1, 3, 5, 9, 15, 17, 21, 27, 31, 33, 45
0, 1, 2, 4, 8, 10, 13, 16, 20, 23, 26, 28

Last time I posted a sequence, someone (in violation of both the rules and the spirit of the question) went to the On-Line Encyclopedia of Integer Sequences to get the answer. Well, this time, that won’t work. The first sequence is not there. That database is having trouble right now, so I can’t query about the second, but because of their relationship, if the first isn’t there, the second is very unlikely to be either.

If no one gets the answers, I’ll post them in about three days.

2

As a quick hint, can you confirm that the solutions are purely mathematically based?

3

Not purely. Here’s a hint: convert the numbers to another base

4

Is there anything mathematically interesting about these sequences?

Obviously any series of n integers can be generated by constructing a polynomial of order n.

And most puzzles of this type rely on some ‘cute trick’ such as each term being the ASCII representation of the first letter in each word of something like War and Peace… not really very interesting….

5

0, 1, 3, 5, 9, 15, 17, 21, 27, 31, 33, 45
0, 1, 11, 101, 1111, 10001, 10101, 100001, 101101. All palindromes in base 2, 111 is missing though

0, 1, 2, 4, 8, 10, 13, 16, 20, 23, 26, 28
0, 1, 2, 11, 22, 101, 111 121, 202, 212, 222, 1001.
Palindromes in base 3

6

This is the correct answer and the answer for the other sequence is also correct. The missing number was a mistake on my part (and note you missed one as well).