Abstract: Habib Lebsir studied three-term arithmetic progressions in the square intervals [nZ,(n+1)Z) and focused on progressions whose arithmetic mean is nZ+n-1, nZ+n, or nZ+n+1. His paper reports this pattern for the first 100 intervals and presents its continuation as a conjecture. When this geometry is applied to the MRB constant, the middle quantity nZ+n=n(n+1) becomes the exact center of a natural square block of the defining alternating nth-root series. This observation yields a symmetric block decomposition, a curvature correction with faster decay, and an Euler-polynomial description of the block coefficients. The purpose of this note is to record that connection carefully and to explain why it may be useful in the continuing rationality problem for the MRB constant.