Error propagation between add by pair and sum by index order

I want to find out a sequence Bₓ(x=1,....,n) where there are accuracy difference between the summation of indexed order and the summation when added by pairs.

I know added up by pairs give more digit of accuracy. But I can't find proper algorithm to solved this. Here is a example:

1. B₁+ B2 + B3 + B4(summation of index order)
2. p= (B1+B2), q= (B3+B4) r= p+q

I need the sequence where 2 has more accuracy than 1