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 +, -, *, /.

1, 2, 4, 10, 29, 76, 284, 1413, 7187, 38103, 231051, 1765186, 10539427

Offset: 1

Author

Jean-Marc Rebert, Mar 28 2001

Keywords

• hard
• nonn

Comments

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

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

a(13) has now been verified by computer. - Zhao Hui Du, Nov 05 2008

Examples

			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.
		

Links

• Gilles Bannay, Countdown Problem (to obtain a(4)=10 for example, enter ceb -a4 -x1 0 1 2 3)
• Michael S. Branicky, Python program for OEIS A060315 and its +,-,* version
• Zhao Hui Du, The C++ source code to find the smallest integer [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]
• Zhao Hui Du, The webpage where the result is posted [From _Zhao Hui Du_, Oct 08 2008]
• Index entries for similar sequences

Crossrefs

Cf. A060316, A141494, A354423.

Formula

a(n) >= A354423(n-1). - Michael S. Branicky, Jun 05 2022

Extensions

More terms from Koksal Karakus (karakusk(AT)hotmail.com), May 26 2002

One more term from Zhao Hui Du, Oct 08 2008

Replaced two broken links with a link to a local copy of the missing program. - N. J. A. Sloane, Jul 04 2022