Search: id:A060315
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%I A060315
%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 same as this 
               sequence. It takes the program two days to find the result for n=11. 
               We still don't know whether the two sequences are same for n greater 
               than 11. [From Du, Zhao Hui (zhao.hui.du(AT)gmail.com), Oct 01 2008]
%C A060315 The first 12 items are the same as the result of using all number 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) [From Du, Zhao Hui (zhao.hui.du(AT)gmail.com), 
               Oct 08 2008]
%C A060315 The 13th item has now been verified by computer [From Du, Zhao Hui (zhao.hui.du(AT)gmail.com), 
               Nov 05 2008]
%H A060315 G. Bannay, <a href="http://mapage.noos.fr/gbannay/jeux.html">LE COMPTE 
               EST BON</a> (to obtain a(4)=10 for example, enter ceb -a4 -x1 0 1 
               2 3)
%H A060315 <a href="Sindx_Fo.html#4x4">Index entries for similar sequences</a>
%H A060315 <a href="http://www.mitbbs.cn/bbsann2/scitech.faq/Science/Amusement/24points/
               M.1018110019.A/Re:%20yes....1413"> The C++ source code to find the 
               smallest integer</a> [From Du, Zhao Hui (zhao.hui.du(AT)gmail.com), 
               Oct 01 2008]
%H A060315 Du, Zhao Hui, <a href="http://bbs.emath.ac.cn/viewthread.php?tid=705&page=15&fromuid=20#pid10404">
               The webpage where the result is posted</a> [From Du, Zhao Hui (zhao.hui.du(AT)gmail.com), 
               Oct 08 2008]
%H A060315 <a href="http://zdu.spaces.live.com/blog/cns!C95152CB25EF2037!165.entry">
               Link to the result</a> [From Du, Zhao Hui (zhao.hui.du(AT)gmail.com), 
               Nov 05 2008]
%e A060315 For n=4 we have {0,1,2,3} to play with 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.
%Y A060315 Cf. A141494.
%Y A060315 Sequence in context: A003223 A061417 A153921 this_sequence A148111 A148112 
               A148113
%Y A060315 Adjacent sequences: A060312 A060313 A060314 this_sequence A060316 A060317 
               A060318
%K A060315 hard,nonn
%O A060315 1,2
%A A060315 Jean-Marc Rebert (jm.rebert(AT)calixo.net), Mar 28 2001
%E A060315 More terms from Koksal Karakus (karakusk(AT)hotmail.com), May 26 2002
%E A060315 One more term from Du, Zhao Hui (zhao.hui.du(AT)gmail.com), Oct 08 2008

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