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Count with me (Posted on 2005-05-26) Difficulty: 2 of 5
1,1,2,1,3,2,4,1,4,3,5,2,6,4,?

See The Solution Submitted by Tristan    
Rating: 4.2500 (4 votes)

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Solution Puzzle Solution Comment 16 of 16 |
(In reply to Answer by K Sengupta)

Let us denote the ith term of the sequence by T(i).

Let S(j) be the jth prime number, so that S(1) = 2, S(2) = 3,
S(3) = 5, S(4) = 7, ...and so on.

Then, in terms of the given sequence, we observe that:

T(S(j)) = j, and:
T(S(i1)*S(i2).....S(ip)) = i1*i2*i3.....*ip, with i1< i2< .....< ip,  --------- (i)

We are required to find the 15th term of the given sequence.

Now, 15 = 3*5, so that: (S(i1), S(i2)) = (3, 5), giving: (i1, i2) = (2,3), and accordingly:

T(3*5) = 2*3 = 6

Consequently, the required value corresponding to the mark of interrogation is 6.


  Posted by K Sengupta on 2008-11-02 01:15:45
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