Question 1058638: What's the next number in the series?
4, 12, 13, 15, 14, 10, 11, 9 ...
Found 4 solutions by Alan3354, math_helper, rothauserc, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! What's the next number in the series?
4, 12, 13, 15, 14, 10, 11, 9 ...
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It's 8.
---
0100 4
1100 12
1101 13
1111 15
1110 14
1010 10
1011 11
1001 9
1000 8
It's Gray Code, or reflected binary code.
1 bit changes at each transition.
For the 4 bits:
0
1
3
2
6
7
5
4
C
D
F
E
A
B
9
8
then
18
19
1B
1A
1E
etc.
Answer by math_helper(2461)  (Show Source):
Answer by rothauserc(4718)  (Show Source):
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
The answer is 8. I'll explain why.
4, 12, 13, 15, 14, 10, 11, 9 ...
This is a subsequence of the sequence of binary gray codes
converted to base ten. The sequence of gray codes
beginning with 0 converted to base 10 is:
0,1,3,2,6,7,5,4,12,13,15,14,10,11,9,8,24,25,27,26,30,31,29,...
The binary gray codes are below. Each is considered as having
an arbitrary number of 0's in front:
0...00000 which converted to base 10 is 0
0...00001 which converted to base 10 is 1
0...00011 which converted to base 10 is 3
0...00010 which converted to base 10 is 2
0...00110 which converted to base 10 is 6
0...00111 which converted to base 10 is 7
0...00101 which converted to base 10 is 5
0...00100 which converted to base 10 is 4 <-- your sequence starts here.
0...01100 which converted to base 10 is 12
0...01101 which converted to base 10 is 13
0...01111 which converted to base 10 is 15
0...01110 which converted to base 10 is 14
0...01010 which converted to base 10 is 10
0...01011 which converted to base 10 is 11
0...01001 which converted to base 10 is 9
0...01000 which converted to base 10 is 8 <-- the next one after the 9.
0...11000 which converted to base 10 is 24
0...11001 which converted to base 10 is 25
0...11010 which converted to base 10 is 27
...,
Rule for obtaining any gray code from the
preceding gray code:
Change the digit which is farthest to the right
WHICH DOES NOT GIVE A PREVIOUS GRAY CODE, from
a 0 to a 1, or from a 1 to a 0.
Edwin
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