  For X a simply-connected finite H-space, there is a Bousfield-Kan spectral
sequence which converges to the homotopy of its K-completion. When
X=Spin(2n+1), we expect that these homotopy groups equal the v1-periodic
homotopy groups in dimension greater than n^2. In this paper, we accomplish two
things. (1) We prove that, for any X, the 1-line of this spectral sequence is
determined in an explicit way from K-theory and Adams operations. (2) For
X=Spin(2n+1), we make an explicit computation of this 1-line.
