Posted by **Mathslover** on Friday, May 24, 2013 at 1:48am.

The sequence {ak}112 (base)k=1 satisfies a1=1 and an=1337+n/an−1, for all positive integers n. Let

S=⌊a10a13+a11a14+a12a15+⋯+a109a112⌋.

Find the remainder when S is divided by 1000.

Details and assumptions

The function ⌊x⌋:R→Z refers to the greatest integer smaller than or equal to x. For example ⌊2.3⌋=2 and ⌊−5⌋=−5.

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