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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 +, -, *.

%I A141494 #11 May 30 2018 05:06:00
%S A141494 1,2,5,18,70,406
%N 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 +, -, *.
%C A141494 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.
%C A141494 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.
%e A141494 a(4)=18 because every integer can be calculated up to 17, using the optimal numbers {2,3,10}.
%e A141494 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}.
%e A141494 a(6)=406 because every integer can be calculated up to 405, using the optimal numbers {2,3,4,84,111}.
%Y A141494 Cf. A060315, A142153.
%K A141494 hard,nonn
%O A141494 1,2
%A A141494 _Gilles A.Fleury_, Aug 10 2008, Aug 24 2008; revised Oct 05 2008