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%I #12 Aug 14 2020 13:12:53
%S 2,2,5,11,18,50,131,226,438
%N Smallest positive integer than cannot be obtained from exactly n copies of n using parentheses and the operations +, -, /, *, ^ and concatenation.
%C Only the original numbers may be concatenated, not the results of arithmetic operations (but see A078413).
%C Sequence is infinite. There are a finite number of expressions including n copies of n and various arithmetic operations. Hence A078405(n) is defined for any n. There is a trivial upper bound: A078405(n) < (n-1)! * 6^(n-1). - _Max Alekseyev_, Apr 17 2005
%H Erich Friedman, <a href="https://erich-friedman.github.io/mathmagic/1299.html">Math Magic: Problem of the Month (December 1999)</a> (Possible inspiration for this sequence)
%H <a href="/index/Fo#4x4">Index entries for similar sequences</a>
%e With three 3's one can form 1=(3/3)^3, 2=3-3/3, 3=3+3-3, 4=3+3/3, but not 5, so a(3)=5.
%e With four 4's one can get 1=44/44, 2=4/4+4/4, 3=4-(4/4)^4, 4=4+(4-4)^4, 5=4+(4/4)^4, 6=(4+4)/4+4, 7=44/4-4, 8=4+4+4-4, 9=4+4+4/4, 10=(44-4)/4, but not 11, so a(4)=11.
%Y Cf. A078413.
%K nonn,base
%O 1,1
%A Kit Vongmahadlek (kit119(AT)yahoo.com), Dec 27 2002
%E a(7), a(8) and a(9) computed by Joseph DeVincentis (devjoe(AT)yahoo.com), Dec 27 2002
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