Claims

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1937_12_01_rohrbach: Rohrbach (Math. Z. 42 (1937)) proves g(n) < 2 sqrt(n) for n > 1 by an explicit basis, and n < 0.4992 k^2 for large k, so g(n)^2 > 2.0032 n for large n in Problem 791; refereed.

1976_11_01_hammerer_hofmeister: Hämmerer and Hofmeister (J. Reine Angew. Math. 1976) build 2-bases of k positive elements with range above (10/9)(k^2/4), so g(n)^2 ≤ (18/5 + o(1)) n and the guess g(n) ~ 2 n^{1/2} of Problem 791 is false; refereed.

1979_04_01_mrose: Mrose's 1979 construction of finite additive 2-bases of k elements with range at least (8/7)(k/2)^2 + O(k), so that g(n)^2 ≤ (7/2 + o(1)) n and the guess g(n) ~ 2 n^{1/2} of Problem 791 is false; refereed and credited by the site.

2015_11_01_yu: Yu (J. Number Theory 156 (2015)) proves limsup n(k)/k^2 ≤ 0.4585 for the maximal range of a 2-basis of size k, so g(n)^2 ≥ (1/0.4585 - o(1)) n in Problem 791; refereed.

2016_06_15_kohonen: Kohonen (J. Number Theory 174 (2017)) proves liminf n(k)/k^2 ≥ 85/294 for the maximal range of a 2-basis of size k, so g(n)^2 ≤ (294/85 + o(1)) n in Problem 791; refereed.

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