14, 34, 42, 72, ___
Don’t confine yourself to mathematics. First one with the correct answer gets to come up with a number series of their own. And, hopefully, so on. 
The first two are some number followed by 4. The second two are some number followed by 2, which is half of 4. Therefore the next number is some number followed by 1, which is half of two.
That’s my answer.
96 is the correct answer. It is the station stops for the #2 & #3 subway cars in New York City
You got it, Briminator. You’re up.
96 is the correct answer. It is the station stops for the #2 & #3 subway cars in New York City. I’ll figure out another puzzle in a bit.
::scurries back to work::
Cripes, those of us outside NYC are supposed to be able to figure that out? How about a REAL number sequence?
You New Yorkers are SO provincial! 
Slightly ‘Off Topic’ but how many bus stops are there between Oxford and Stratford? The winner gets to specify his or her bus route.
The hell you say; I’m an Oregonian! (Though I am, um, summering in Manhattan.) Anyway, the beauty of this board is that no matter how obscure or specialized a number sequence (retired jerseys by the Edmonton Oilers, for example), somebody will come along and figure it out.
But no more NYC-centric series from me, dropzone; I promise.
Better not, or I’ll start on exits on the Dan Ryan.
All right, here’s another of 'em while we’re waiting for Brim:
14, 15, 92, 65, ___
I got plenty.
Here’s an old one, but I like it:
1
11
21
1211
111221
312211
13112221
What’s the next line?
Let’s try this.
Count the digits of the first number:
one 1, one three, two one’s, three two’s, two one’s.
So next after 13112221 is 1113213211