The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.

Numbers in this sequence are numbers of the form k^2 + m where m is fairly small compared to k^2 and less than 2k + 1. For m < 2k + 1, if k^2 + m isn't in the sequence then k^2 + m + 1 isn't either. Conjecture: 1 <= m <= t for some t < 2k+1. (End)