What is the rule of forming the following sequence : 0,1,10,2,100,11,1000,3,20,101,10000,12,100000,1001,110,4,1000000,21,......
The last digit is the power of 2 in the factorization of the number. The digit before that is the power of 3. The digit before that is the power of 5. It keeps going with all of the primes.
1=2^0
2=2^1
3=3^1*2^0
4=2^2
5=5^1*3^0*2^0
6=3^1*2^1
7=7^1*5^0*3^0*2^0
8=2^3
9=3^2*2^0
10=5^1*3^0*2^1
11=11^1*7^0*5^0*3^0*2^0
12=3^1*2^2
13=13^1*11^0*7^0*5^0*3^0*2^0
14=7^1*5^0*3^0*2^1
15=5^1*3^1*2^0
16=2^4
17=17^1*13^0*11^0*7^0*5^0*3^0*2^0
18=3^2*2^1
19=19^1*17^0*13^0*11^0*7^0*5^0*3^0*2^0
Therefore, the next number is 10000000.

Posted by Math Man
on 20130916 23:11:42 