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A060315 a(1)=1; a(n) is the smallest positive integer that cannot be obtained from the integers {0, 1, ..., n-1} using each number at most once and the operators +, -, *, /.

%I A060315 #46 Dec 29 2022 11:10:01
%S A060315 1,2,4,10,29,76,284,1413,7187,38103,231051,1765186,10539427
%N A060315 a(1)=1; a(n) is the smallest positive integer that cannot be obtained from the integers {0, 1, ..., n-1} using each number at most once and the operators +, -, *, /.
%C A060315 I had written a C++ program to find the smallest positive integer that cannot be obtained from the integers {1,2,...,n-1} using each number exactly once and the operators +,-,*,/. The result is the same as this sequence through n=11. It takes the program two days to find the result for n=11. We still don't know whether the two sequences are the same for n greater than 11. - _Zhao Hui Du_, Oct 01 2008
%C A060315 The first 12 terms are the same as the result of using all numbers from 0 to n-1 exactly once and only the operators +,-,* (so we could get all integers less than a(n) without the operator /). The minimal number which could not be reached using all numbers from 0 to 12 exactly once and only operators +,-,* is 10539427. But I have still not verified whether it is a(13). - _Zhao Hui Du_, Oct 08 2008
%C A060315 a(13) has now been verified by computer. - _Zhao Hui Du_, Nov 05 2008
%H A060315 Gilles Bannay, <a href="https://web.archive.org/web/20061201125224/http://gilles.bannay.free.fr/jeux_us.html">Countdown Problem</a> (to obtain a(4)=10 for example, enter ceb -a4 -x1 0 1 2 3)
%H A060315 Michael S. Branicky, <a href="/A060315/a060315.py.txt">Python program for OEIS A060315 and its +,-,* version</a>
%H A060315 Zhao Hui Du, <a href="/A060315/a060315.pdf">The C++ source code to find the smallest integer</a> [The old link to the program was broken, but _Zhao Hui Du_ kindly sent this email with a copy of the code. - _N. J. A. Sloane_, Jul 04 2022]
%H A060315 Zhao Hui Du, <a href="http://bbs.emath.ac.cn/viewthread.php?tid=705&amp;page=15&amp;fromuid=20#pid10404">The webpage where the result is posted</a> [From _Zhao Hui Du_, Oct 08 2008]
%H A060315 <a href="/index/Fo#4x4">Index entries for similar sequences</a>
%F A060315 a(n) >= A354423(n-1). - _Michael S. Branicky_, Jun 05 2022
%e A060315 For n=4 the numbers available for use are {0,1,2,3} and we can get 6=2*3, 7=2*3+1, 8=2*(1+3), 9=3*(1+2), but we cannot get 10, hence a(4) = 10.
%Y A060315 Cf. A060316, A141494, A354423.
%K A060315 hard,nonn
%O A060315 1,2
%A A060315 _Jean-Marc Rebert_, Mar 28 2001
%E A060315 More terms from Koksal Karakus (karakusk(AT)hotmail.com), May 26 2002
%E A060315 One more term from _Zhao Hui Du_, Oct 08 2008
%E A060315 Replaced two broken links with a link to a local copy of the missing program. - _N. J. A. Sloane_, Jul 04 2022