What are the next two numbers in this sequence?
1, 1, 7, 3, 23, 23, 111, 15, 351, 415, __, __

(In reply to Some help - binary! by GOM)

Those were my thoughts exactly. I did my master's thesis on encryption, so I almost immediately think in other number bases. I tried base 8, noticing no individual number was higher than 7, but it didn't help me much. Then I went to binary, and noticed each pair had an increasing number of 1's in the least significant bits. So, by this pattern, the last two numbers have at least six consecutive 1's in the lower positions.

Then I went to Radix 4 to group pairs of bits within each number. This gives you:

1.    00 00 01
2.    00 00 01
3.    00 00 13
4.    00 00 03
5.    00 01 13
6.    00 01 13
7.    00 12 33
8.    00 00 33
9.    01 11 33
10.   01 21 33
11.   xx x3 33
12.   xx x3 33

...Which doesn't give you much, and that's where I'm at.

 

 

Posted by Eric on 2004-06-07 13:17:27