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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 +, -, *, /. 19
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 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. [Du, Zhao Hui, Oct 01 2008]

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). [Du, Zhao Hui, Oct 08 2008]

The 13th item has now been verified by computer. [Du, Zhao Hui, Nov 05 2008]

LINKS

Table of n, a(n) for n=1..13.

G. Bannay, LE COMPTE EST BON (to obtain a(4)=10 for example, enter ceb -a4 -x1 0 1 2 3)

The C++ source code to find the smallest integer [From Du, Zhao Hui, Oct 01 2008]

Du, Zhao Hui, The webpage where the result is posted [From Du, Zhao Hui, Oct 08 2008]

Link to the result [From Du, Zhao Hui, Nov 05 2008]

Index entries for similar sequences

EXAMPLE

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.

CROSSREFS

Cf. A060316.

Cf. A141494.

Sequence in context: A061417 A153921 A189582 * A148111 A148112 A224845

Adjacent sequences:  A060312 A060313 A060314 * A060316 A060317 A060318

KEYWORD

hard,nonn

AUTHOR

Jean-Marc Rebert, Mar 28 2001

EXTENSIONS

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

One more term from Du, Zhao Hui, Oct 08 2008

STATUS

approved

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Last modified April 25 00:32 EDT 2017. Contains 285346 sequences.