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Hey guys, I recently stumbled across this interesting sequence:

1, 3, 5, 11, 17, 39, 65, 139, 261, 531, 1025, 2095, 4097, 8259, 16405, 32907, 65537, 131367, 262145 ...

Any ideas? The sequence appears to somewhat resemble the binary sequence.

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closed as off topic by Steve Huntsman, Denis Serre, François G. Dorais Jun 5 '11 at 10:53

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After 262145, it seems to take constantly the value 14. Very strange. Very strange indeed. – Mariano Suárez-Alvarez Jun 5 '11 at 5:07
Not entirely sure what you mean, where did you obtain this result? – abc123def456 Jun 5 '11 at 5:13
@Mariano means that there's no well defined way of extending a finite sequence of numbers to an infinite sequence. Of course, some extensions are "better" than others. – Simon Jun 5 '11 at 5:16
You are absolutely right! In retrospect, I have proposed a rather impossible task with my original question. – abc123def456 Jun 5 '11 at 5:22
up vote 4 down vote accepted

I would try this:

$$ a(n) = \sum_{k, k|n } 2^{(k-1)}$$

In Mathematica syntax this is (see W|A)

 Sum[2^(k - 1), {k, Divisors[n]}]
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Thank you, just what I was looking for. – abc123def456 Jun 5 '11 at 5:10
@abc123 Not a problem. The OEIS is a very handy resource. – Simon Jun 5 '11 at 5:17

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