A142153 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 operators +, -, *, /.

1, 2, 5, 18, 87, 451

Offset: 1

Author

Gilles A.Fleury, 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)=3495, a(8)=32355, a(9)=384289. If anyone has found higher numbers please contact me. - updated by Gilles A.Fleury, Jul 10 2017 and May 22 2018

Examples

			a(4) = 18 because every integer can be calculated up to 17, using one of the four (!) optimal sequences {2,3,10} or {2,3,14} or {2,6,11} or {2,6,13}.
a(5) = 87 because every integer can be calculated up to 86, using the optimal numbers {2,3,14,60}.
a(6) = 451 because every integer can be calculated up to 450, using the optimal numbers {2,3,4,63,152}. - _Gilles A.Fleury_, Mar 06 2009
		

Crossrefs

Cf. A141494, A060315.

Extensions

a(6) from Gilles A.Fleury, Mar 06 2009