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

The sequence is the base 10 conversion of a binary sequence of numbers (zero-leading permitted) where each n column of left-justified binary digits alternates between a sequence of n 1's followed by n 0's beginning with the nth term.

   1 : 1
   1 : 01
   7 : 111
   3 : 0011
  23 : 10111
  23 : 010111
 111 : 1101111
  15 : 00001111
 351 : 101011111
 415 : 0110011111
The next four numbers of the sequence is then...
1855 : 11100111111     <-- *
 319 : 000100111111    <-- *
4735 : 1001001111111
5247 : 01010001111111
....

*The two numbers of the sequence sought are 1855, 319.

Posted by Dej Mar on 2008-09-29 12:13:14