%I A071794
%S A071794 2,4,11,34,178,926,9434
%N A071794 a(n) is the smallest integer > 0 that cannot be obtained from the integers 
               {1, ..., n} using each number at most once and the operators +, -, 
               *, /, ^.
%C A071794 The old entry a(6) = 791 was incorrect since 791 = (2^5 + 3^4) (1+6). 
               - Bruce Torrence (btorrenc(AT)rmc.edu), Feb 14 2007. Also 791 = ((3*5)^4-1)/
               2^6. - Sam Handler (shandler(AT)macalester.edu) and Kurt Bachtold 
               (kbachtold(AT)route24.net), Feb 28 2007.
%C A071794 I believe that a(7) = 9434 (with approximately 98% certainty). - Bruce 
               Torrence (btorrenc(AT)rmc.edu), Feb 14 2007
%C A071794 Using the Java programming language, my brother and I have independently 
               created 2 programs which absolutely solve this problem for a given 
               index via brute force algorithms. Our process is to systematically 
               generate every possible equation in polish notation, solve it, then 
               add its solution (providing that it is a positive integer) to a list 
               of previous solutions. After all solutions have been calculated, 
               the program references the list to find the lowest missing number. 
               - Michael and David Kent (zdz.ruai(AT)gmail.com), Jul 29 2007
%D A071794 B. Torrence, Arithmetic Combinations, Mathematica in Education and Research, 
               Vol. 12, No. 1 (2007), pp. 47-59.
%H A071794 <a href="Sindx_Fo.html#4x4">Index entries for similar sequences</a>
%e A071794 a(3)=11 because using {1,2,3} we can write 1, 2, 3, 3+1=4, 3+2=5, 3*2=6, 
               3*2+1=7, 2^3=8, 3^2=9, (3^2)+1=10 but we cannot obtain 11 in the 
               same way.
%t A071794 The Torrence article gives a description of how one can use Mathematica 
               to investigate the sequence.
%Y A071794 Cf. A060315.
%Y A071794 Sequence in context: A076321 A126149 A000088 this_sequence A107378 A086611 
               A035098
%Y A071794 Adjacent sequences: A071791 A071792 A071793 this_sequence A071795 A071796 
               A071797
%K A071794 hard,more,nonn
%O A071794 1,1
%A A071794 Koksal Karakus (karakusk(AT)hotmail.com), Jun 06 2002
%E A071794 a(6) corrected by Bruce Torrence (btorrenc(AT)rmc.edu), Feb 14 2007
%E A071794 a(7) from Michael and David Kent (zdz.ruai(AT)gmail.com), Jul 29 2007