A275489 Most consecutive numbers that can be covered with arithmetic progressions of differences 2i+1, 1<=i<=n.

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

Offset: 1

Author

Robert Israel, Jul 29 2016

Keywords

• nonn
• more

Comments

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.

Examples

			[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.
		

Links

• Wikipedia, Covering system.