The Algebra of Warp

Not sure if I posted this here before … so here goes.

A few days back I was meandering through my backlog of writings (a couple hundred Word docs in a half-dozen places with completely unhelpful titles that must have seemed awfully witty at the time). I came across a math problem that I can’t figure out if I made it up or wrote about it after reading it. I think the latter, because I think it has something to do with Warp drives and the speed of light.

　

Assume:

　

w(1) = c

w(2) = ?

w(3) = 24c

w(4) = ?

w(5) = ?

w(6) = 512c

　

Questions:

Is there enough information to determine what expression w(x) can be?

Is there enough information to determine the values of the question marks?

If yes, what is it / what are they?