cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

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 +, -, *, /.

Original entry on oeis.org

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

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Author

Jean-Marc Rebert, Mar 28 2001

Keywords

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

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

A071110 a(n) is the smallest integer >=0 we cannot obtain from n, n+1, n+2, n+3, n+4 and the operators +, -, *, /, using each number only once.

Original entry on oeis.org

29, 76, 141, 172, 193, 197, 205, 211, 245, 181, 162, 85, 86, 69, 71, 61, 62, 67, 52, 53, 58, 58, 58, 59, 62, 45, 46, 49, 20, 51, 7, 22, 10, 7, 10, 7, 7, 7, 7, 15, 12, 13, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 10, 7, 7, 7, 7, 7, 7, 10, 7, 7, 7, 7, 7, 7, 7, 7, 7
Offset: 0

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Author

Koksal Karakus (karakusk(AT)hotmail.com), May 27 2002

Keywords

Comments

It seems that a(n)=7 for all n>=62, but this needs to be proved.

Examples

			a(61)=10 because by using 61, 62, 63, 64, 65 we can get 62-61=1, 63-61=2, ..., 63/((64-61)*(65-62))=7, (65-61)*(64+62)/63=8, (65-62)*(64-61)=9 but we cannot obtain 10 in the same way.
a(32) != 7 because 7 = 35 / (34 - (32 - (36 - 33))). - _Sean A. Irvine_, Jun 30 2024

Links

Crossrefs

Cf. A060316.

Extensions

a(32) and a(40) corrected by Sean A. Irvine, Jun 30 2024

A143191 a(n) is the smallest natural number we cannot obtain from n, n+1, n+2, n+3, n+4, n+5, n+6 and the operators +, -, *, /, using each number only once.

Original entry on oeis.org

284, 1413, 2113, 3266, 4943, 6242, 9105, 11586, 6269, 6427, 8407, 8406, 9224, 11079, 12451, 8392, 3469, 4253, 4043, 4126, 4087, 4657, 4330, 4639, 5114, 3983, 5839, 4415, 6376, 4537, 5231, 5161, 4090, 3199, 2057, 3372, 2285, 2270, 2525, 2609, 2590, 1209
Offset: 0

Views

Author

Gilles A.Fleury, Oct 18 2008

Keywords

Comments

This sequence is related to the sequences A071110 (for 5 successive integers) and A060316 (for 6 successive integers) and others sequences to come...
Asymptotically, the sequence tends to 29 (the first n for which a(n)=29 is n=249).

Links

Crossrefs

Cf. A071110, A060316, A071107, A060315, A141494, A142153.

A143192 a(n) is the smallest natural number we cannot obtain from n, n+1, n+2, n+3, n+4, n+5, n+6, n+7 and the operators +, -, *, /, using each number only once.

Original entry on oeis.org

1413, 7187, 12421, 22751, 28862, 48046, 36094, 46372, 54214, 72845, 88119, 107246, 125589, 104153, 43838, 45893, 55054, 62090, 66226, 70187, 69638, 74941, 85303, 81913, 68891, 77237, 37997, 48758, 42827, 45554, 22217, 26617, 29422, 29099
Offset: 0

Views

Author

Gilles A.Fleury, Oct 18 2008, Mar 06 2009

Keywords

Comments

This sequence is related to the sequences A071110 (for 5 successive integers) and A060316 (for 6 successive integers) and others sequences to come...
Asymptotically the sequence tends to 67 (the first n for which a(n)=67 is n=1042).

Links

Crossrefs

Cf. A071110, A060316, A071107, A060315, A141494, A142153.

A143193 a(n) is the smallest natural number we cannot obtain from n, n+1, n+2, n+3, n+4, n+5, n+6, n+7, n+8 and the operators +, -, *, /, using each number only once.

Original entry on oeis.org

7187, 38103, 54251, 114358, 168673, 264111, 319699, 456061, 588847, 812092, 1005321, 1222630, 445059, 499063, 600907, 706847, 820609, 929113, 1048137, 1269847, 1049291, 1113439, 1252843, 1411942, 1588841, 456206, 462382, 464357, 479894
Offset: 1

Views

Author

Gilles A.Fleury, Oct 18 2008

Keywords

Comments

This sequence is related to the sequences A071110 (for 5 successive integers) and A060316 (for 6 successive integers).
What is the asymptotic value of this sequence? What is the first n for which a(n) equals the asymptotic value?

Links

Crossrefs

Cf. A071110, A060316, A071107, A060315, A141494, A142153.

A071905 a(n) is the smallest positive integer (which is a polynomial of degree 0) that cannot be obtained using the polynomials {x, x+1, ..., x+n} using each polynomial at most once and the operations +, -, *, /.

Original entry on oeis.org

1, 2, 3, 5, 7, 13, 29, 67, 103, 373
Offset: 0

Views

Author

Koksal Karakus (karakusk(AT)hotmail.com), Jun 13 2002

Keywords

Examples

			a(3)=5 because using {x, x+1, x+2, x+3} we can get x+1-x=1, x+2-x=2, x+3-x=3, (x+2-x)*(x+3-(x+1))=4 but we cannot obtain 5 in the same way.

Links

Crossrefs

Cf. A060315, A060316, A071110.

A143190 a(n) is the smallest natural number we cannot obtain from n, n+1, n+2, n+3 and the operators +, -, *, /, using each number only once.

Original entry on oeis.org

10, 29, 41, 43, 40, 44, 26, 21, 15, 15, 18, 18, 18, 10, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
Offset: 1

Views

Author

Gilles A.Fleury, Oct 18 2008

Keywords

Comments

This sequence is related to the sequences A071110 (for 5 successive integers) and A060316 (for 6 successive integers) and others sequences to come...
Asymptotically (in fact as soon as n>=15), the sequence tends to 5.

Crossrefs

Cf. A071110, A060316, A071107, A060315, A141494, A142153.
Showing 1-7 of 7 results.

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