A260818 - OEIS

A260818

Maximal m such that a polynomial P = Sum_{k=0..m} x^{d(k)} with 0 = d(0) < ... < d(m) has P^2 = Sum_{k>=0} B(k) x^k with B(k) <= n for all k and B(k) > 0 for k <= d(m).

%I #7 Aug 02 2015 06:24:05

%S 1,3,5,12,14,35,41

%N Maximal m such that a polynomial P = Sum_{k=0..m} x^{d(k)} with 0 = d(0) < ... < d(m) has P^2 = Sum_{k>=0} B(k) x^k with B(k) <= n for all k and B(k) > 0 for k <= d(m).

%C See the main entry A260551 for further comments and references, and A260817 for the maximal degree d(m) of such polynomials.

%H Peter Borwein, Stephen Choi and Frank Chu, <a href="http://dx.doi.org/10.1090/S0025-5718-05-01777-1">An old conjecture of Erdös-Turán on additive bases</a>, Math. Comp. 75 (2006), 475-484, see Table 1 p. 481.

%K nonn,hard,more

%O 1,2

%A _M. F. Hasler_, Jul 31 2015