Setting an initial value for ListAnimate?

Question

ListAnimate is fairly similar to Manipulate, but while Manipulate has a simple way to request an initial value for the manipulation parameter, I haven't found a way to tell ListAnimate to start with a certain value.

Consider a simple example:

ListAnimate[Table[Plot[Sin[p x], {x, -1, 1}], {p, 1, 4}]]  

vs.

Manipulate[Plot[Sin[p x], {x, -1, 1}], {p, Range[1, 4]}]  

These simple examples seem virtually the same (I didn't bother to change the Manipulate Control to a slider), but in fact, they are different. ListAnimate is essentially pre-compiled. In my research, I want to do something similar with very complex plots which take a long time to produce. Manipulate re-calculates it's arguments when the manipulator is adjusted. We don't notice it here because Sin[p x] is so trivial. But with a complicated plot, it's no good. Conversely, with ListAnimate, it may take 15 minutes or more to run the code, once and for all, and then I can quickly scan through all the output smoothly.

I looked through the options for ListAnimate and, for example, I can begin the output paused with ,AnimationRunning -> False.

Is there a way to make the animation begin with not the first element but a chosen one?

TL;DR

Make

ListAnimate[Table[Plot[Sin[p x], {x, -1, 1}], {p, 1, 4}], AnimationRunning -> False]  

begin with output of Plot[Sin[3 x], {x, -1, 1}]

Answer 1

As commented by Dr. belisarius

You can set the initial value by creating the following sentence: {p, 3}.

Animate[Plot[Sin[p x], {x, -1, 1}], {{p, 3}, 1, 4, 1}, 
 AnimationRunning -> False]