A141494 a(n) is the "highest smallest" positive integer that cannot be obtained from the (n-1) optimized integers (to be defined for each n) using each number at most once and the three operators +, -, *.

1, 2, 5, 18, 70, 406

Offset: 1

Author

Gilles A.Fleury, Aug 10 2008, Aug 24 2008; revised Oct 05 2008

Keywords

• hard
• nonn

Comments

This sequence is a kind of optimized version of the sequence A060315 for which the inputs are the integers {0,1,...,n-1}. Here the inputs are optimized so that the smallest positive integer, that cannot be obtained, is maximized.

Further terms may be hard to find. Some additional terms (still to be proved) could be a(7)=2876, a(8)=24756, a(9)=346404. If anyone has found higher numbers please contact me.

Examples

			a(4)=18 because every integer can be calculated up to 17, using the optimal numbers {2,3,10}.
a(5)=70 because every integer can be calculated up to 69, using one of the two (!) optimal sequences {2,3,4,27} or {2,3,10,41}.
a(6)=406 because every integer can be calculated up to 405, using the optimal numbers {2,3,4,84,111}.
		

Crossrefs

Cf. A060315, A142153.