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]

OK, post, spoilerised, you suggested key to the pattern.

[spoiler]f(n)=f(n-1)*f(n-3) - f(n-2); for f(1)=3, f(2)=4, f(3)=5[/spoiler]

[spoiler]
f(n)=f(n-1)*f(n-2) - f(n-1) - f(n-2)
[/spoiler]

Ok, here is the way that I derived the sequence. axn1 has the correct sequence, but my formula is simpler.

[spoiler]n[sub]1[/sub]=3, n[sub]2[/sub]=4
n[sub]x[/sub] = (n[sub]x-1[/sub]*n[sub]x-2[/sub]) - (n[sub]x-1[/sub]+n[sub]x-2[/sub])[/spoiler]

[QUOTE=Uncwilly]Ok, here is the way that I derived the sequence. axn1 has the correct sequence, but my formula is simpler.[/QUOTE]

Do you really think so?
[spoiler]The only difference is that your expression adds two pairs of parentheses. I don't see how that counts as simpler.[/spoiler]

something else about this sequence:

[spoiler] Each term is the largest number that cannot be composed by a linear combination of a non-negative number[/spoiler]
[spoiler] of each of the previous two terms (holds at least until 11 39 379)[/spoiler]

[spoiler]I figured this part out back in middle school after a question at the MathCounts countdown [/spoiler]
[spoiler] was what is the largest number that cannot be created by adding 3s and 4s. [/spoiler]

also, could an admin please erase my post above this as the spoiler seems to have made my message on one line only