My off the top of my head sequence.
 

This is a seuqnece that I just came up with. It may be a classical one, but I haven't seen it around. Brainiacs should sit on their hands for a while.
Those that think that they have it, use the spoiler to post the next number.

3, 4, 5, 11, 39, .........

:rolleyes:

[spoiler]
379
[/spoiler]

[spoiler]118[/spoiler]

Some how both of you can't be right. I'll give a bit more time before revealing my answer.

I'd bet mine was wrong. If the sequence is special in some way I'd guess it wasn't my answer which was just a boring polynomial.

my guess
 

[spoiler]184[/spoiler]

[SPOILER]184[/SPOILER]

4 guesses with 2 being the same. Would those that submitted numbers care to also post (spoilerised of course) the next term after that, i.e. the 7th number in the set.?

[spoiler]
14363
[/spoiler]

[spoiler]289[/spoiler]

[spoiler]1985[/spoiler]