Over at http://www.scottaaronson.com/blog/?p=2725#comment-1089004 we had a discussion of intermediate Turing degrees.

The following function came up:

Take Chaitin’s constant, and rearrange its binary digits as follows: for each of the sets {1st digit} {2-3rd digits} {4-7th digits} {2^n-(2^n+1)-1}, order the digits within in ascending order, i.e. zeros then ones.

(This is a number, the function is just {n->nth digit of the number} for natural numbers n)

A later comment says it's non-computable:

because it has unbounded information about omega.

We know that K(Omega_n) >= n + O(1), but knowing how many 0s and 1s are in the second half of n/2 bits would allow you to save about (log n)/2 bits. This gives a contradiction for large enough n of the form n=2^i

It's clearly either of degree 0′ or lower. Which is it? In other words, does an oracle for this function let you solve the halting problem?