|
| |
|
|
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 +, -, *, /.
|
|
22
|
|
|
|
1, 2, 4, 10, 29, 76, 284, 1413, 7187, 38103, 231051, 1765186, 10539427
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
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
|
|
|
LINKS
|
Gilles Bannay, Countdown Problem (to obtain a(4)=10 for example, enter ceb -a4 -x1 0 1 2 3)
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
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.
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
hard,nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
More terms from Koksal Karakus (karakusk(AT)hotmail.com), May 26 2002
Replaced two broken links with a link to a local copy of the missing program. - N. J. A. Sloane, Jul 04 2022
|
|
|
STATUS
|
approved
|
| |
|
|
