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Showing posts from November, 2010

Numerical Sequence Puzzle

What's the next number in this sequence, and how is it determined?

1, 3, 5, 9, 15, 31, 61, 125, 251, 503, 1015, 2035, 4081, 8177, 16367, 32747, 65511, ?

Years ago I spent some time playing around with integer sequence puzzles. I ended up constructing a few puzzles based on ideas I had never seen used before. Sometime between 1995 and 1998 I published four of them in my user profile on the Free Internet Chess Server. Over the years since then I've had a number of people contact me with attempted solutions. A couple dozen or so people were able to solve three of them, but the one shown above remained unsolved for years. Several people submitted solutions that matched as far out as I had revealed terms but diverged later, so I kept publishing more and more terms hoping someone would be able to solve it.

Finally in 2006, someone sent me a solution that matched my sequence as far out as I cared to check. I recently discovered that the puzzle generated more activity than I rea…