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March 5, 2010

1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 ?



What are the next three numbers in the given series?

1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 _ _ _ ?

3 comments:

João Marques said...

1
12
1223
12232334
12232334233445

in each iteration, it repeats the last added numbers, and add the next two number sequence, so it's 445.

(the next iteration would be
1223233423344523344556
)

Eldhose said...

Marques...thanks for your comment...your answer is correct

But I was expecting a different answer

The pattern is - the number of 1's in the binary expansion of the positive integers starting from 1.


#Number #Binary Equivalent #No: of 1's
1 , 1 , 1
2 , 10 , 1
3 , 11 , 2
4 , 100 , 1
5 , 101 , 2
6 , 110 , 2
7 , 111 , 3
8 , 1000 , 1
...........
..........
etc

The next three numbers in the series are 4, 3, 4.

Anonymous said...

5,1,2