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Next Numbers Please #3 (Posted on 2004-06-01) Difficulty: 5 of 5
What are the next two numbers in this sequence?
1, 1, 7, 3, 23, 23, 111, 15, 351, 415, __, __

See The Solution Submitted by Brian Smith    
Rating: 3.9091 (11 votes)

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Hints/Tips Some help - binary! | Comment 10 of 30 |
(In reply to Some thoughts... by Bob)

    109876543210
1.            1        1
2.            1        1
3.          111        7
4.           11        3
5.        10111       23
6.        10111       23
7.      1101111     111
8.         1111       15
9.    101011111     351
10.    110011111     415
11. 100001111111 2175 - Erik's guess
12.   110111111 447 - Erik's guess
11. 11011111111 1791 - Telly's guess

It looks like each successive pair of numbers has the same number of 1's on the right, with one more than the last 2 numbers. Also I think the maximum number of digits to the left of those 1's should increase by one with each pair. Which is why I think Erik's guess for #11 might be too high. If I can break it down further...

0, 0, 1, 0, 10, 10, 110, 0, 1010, 1100, _____, _____...

or in base 10...

0, 0, 1, 0, 2, 2, 6, 0, 10, 12, __, __...

...that might have made it harder :-)

Oh well. I think that if we can find a pattern to those numbers, we might have the answer.


  Posted by Danny on 2004-06-07 10:41:02
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