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 Next Numbers Please (Posted on 2003-07-11)
What are the next two numbers in this sequence? 1, 2, 3, 5, 6, 9, 10, 15, 18, 24, 25, 34, 35, ??, ??

 See The Solution Submitted by Brian Smith Rating: 3.6250 (8 votes)

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 Puzzle Solution With Explanation | Comment 13 of 14 |

Let S(p) denote the pth term of the given sequence.
Then, we observe that the terms of the given sequence are in conformity wih the following recurrence relationship:

S(p) = S(p-1) + S(T(p)), where T(x) denotes the largest divisor of x (excluding x).

Thus,
S(1) + S(T(2)) = 1 + S(2) = 1+ 1 = 2 = S(2)

S(2) + S(T(3) = 2 + S(3) = 2 + 1 = 3 = S(3)

S(3) + S(T(4)) = 3 + S(2) = 3 + 2 = 5 = S(4)

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S(14) = S(13) + S(T(14)) = 35 + S(7) = 35 + 10 = 45

S(15) = S(14) + S(T(15)) = 45 + S(5) = 45 + 6 = 51

Consequently, the required next two numbers in the given sequence are 45 and 51.

 Posted by K Sengupta on 2008-03-29 10:17:16

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