Could there be a number say: A = $0.a_1a_2\cdots a_n$->$a_k \cdots$
where say {$a_1a_2$} and {$a_n$->$a_k$} are computable parts of A. Yet every thing else is not computational.
I imagine a scheme where it takes an infinite amount of computational resources to locate where in the number that set goes and possibly the arrangement/sorting of the set could lead to really big numbers. Yet, the issue is that we still assume that the set before the a(n to k) set is finite, therefore we should be able to compute this.
This leads me to believe that maybe only the trailing ellipsis can be part of the non-computable part. Is this true, or is there a way to put a non-computable sequence into the number while still having some computable parts.
Chaitins constant is a nice example. Take a look at Wolfram Alpha http://mathworld.wolfram.com/ChaitinsConstant.html
You find the first digits of the non-computable constant Ω = 0.0078749969978123844... Go ahead and create your final t-shirt.
But yes the question doesn't make sense, since it is easy to construct such numbers x = π + Ω * 10^-100