Problems & Puzzles: Puzzles

Puzzle 296. An intriguing sequence

Igor Schein sends the following intriguing sequence & puzzle, perhaps very appropriate for the season:

This is part of what he wrote days ago (9/12/04):

I have something that might be suitable as a puzzle for your site.


1) find the next n primes
2) find a closed formula describing this sequence
3) Is it infinite?
4) Is it dense?

I can generate as many terms as I need, but at a high computational cost. I don't know of a closed formula, but I would like to find one...



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