

A060315


a(1)=1; a(n) is the smallest positive integer that cannot be obtained from the integers {0, 1, ..., n1} using each number at most once and the operators +, , *, /.


19



1, 2, 4, 10, 29, 76, 284, 1413, 7187, 38103, 231051, 1765186, 10539427
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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,...,n1} 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 n1 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

JeanMarc 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



