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May 20th, 2013, 08:49 PM   #1
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find an item of series

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May 21st, 2013, 10:14 AM   #2
 
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Re: find an item of series

Every member of S is of the form , and S can be sorted in increasing order as follows: sort by greater z, then by greater y, and then by greater x. Let us consider the number of elements sorting by greater z:

1 element for z = 2





3 elements for z = 3...

elements for z = k.

Thus, up to z = k, there are a total of elements.

The first k such that is 9, so for the 100th element, z = 9.

Now the 120th element is , so we simply work backwards from there:

The 113th element is

The 112th element is

The 106th element is

The 105th element is

The 100th element is .
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