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%I #6 Jul 10 2011 18:42:52
%S 2,4,11,34,178,926,9434
%N 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 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 I believe that a(7) = 9434 (with approximately 98% certainty). - Bruce Torrence (btorrenc(AT)rmc.edu), Feb 14 2007
%C 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 B. Torrence, Arithmetic Combinations, Mathematica in Education and Research, Vol. 12, No. 1 (2007), pp. 47-59.
%H <a href="/index/Fo#4x4">Index entries for similar sequences</a>
%e 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 The Torrence article gives a description of how one can use Mathematica to investigate the sequence.
%Y Cf. A060315.
%K hard,more,nonn
%O 1,1
%A Koksal Karakus (karakusk(AT)hotmail.com), Jun 06 2002
%E a(6) corrected by Bruce Torrence (btorrenc(AT)rmc.edu), Feb 14 2007
%E a(7) from Michael and David Kent (zdz.ruai(AT)gmail.com), Jul 29 2007
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