What are the next few terms in this sequence?

	-
	/-\
	/-\-
	//-\\
	/-\--
	/-\/-\
	/-\---
	///-\\\
	//-\\-
	/-\-/-\

From hint 2 the pattern -, /-\, //-\\, ///-\\\ = 1, 2, 4, 8 became obvious, so I could see that it most likely used exponents. With hint 3 to confirm the bases, it fell into place.

How to read numbers:
Each - is a column entry. The number of "/\"'s surrounding the dash is the value of the column (- is 0, /-\ is 1, //-\\ is 2, etc)
Each column is a prime, starting with the rightmost being 2, the lowest prime.
The entry in the column is the exponent for that prime (e.g, a 0 in the 2's column means 2^0 = 1).
Each column is ultimately multiplied to get the result.

Thus the given sequence would be read:
0: (2^0) = 1
1: (2^1) = 2
1,0: (3^1)*(2^0) = 3
2: (2^2) = 4
1,0,0: (5^1)*(3^0)*(2^0) = 5
1,1: (3^1)*(2^1) = 6
1,0,0,0: (7^1)*(5^0)*(3^0)*(2^0) = 7
3: (2^3) = 8
2,0: (3^2)*(2^0) = 9
1,0,1: (5^1)*(3^0)*(2^1) = 10

So the next few terms are:
/-\----
/-\//-\\
/-\-----
/-\--/-\
/-\/-\-
////-\\\\

Posted by Ender on 2003-06-24 04:46:17