%I #7 Jul 29 2016 21:19:03

%S 1,2,4,6,10,13,17,22,30,38,45,53,63,74,83,96,112,128,145

%N Most consecutive numbers that can be covered with arithmetic progressions of differences 2i+1, 1<=i<=n.

%C Erdos and Selfridge conjecture that there is no covering system whose moduli are distinct odd integers > 1. This is equivalent to saying that a(n) is finite for all n.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Covering_system">Covering system</a>.

%e [1,2,3,4] can be covered by the arithmetic progressions 3k+1, 5k+2 and 7k+3 but [1,2,3,4,5] can't be covered by three arithmetic progressions with differences 3, 5 and 7, so a(3) = 4.

%K nonn,more

%O 1,2

%A _Robert Israel_, Jul 29 2016