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.

User: Gilles A.Fleury

Gilles A.Fleury's wiki page.

Gilles A.Fleury has authored 6 sequences.

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

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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.

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

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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.

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

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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

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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.

A141494 a(n) is the "highest smallest" positive integer that cannot be obtained from the (n-1) optimized integers (to be defined for each n) using each number at most once and the three operators +, -, *.

Original entry on oeis.org

1, 2, 5, 18, 70, 406
Offset: 1

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Author

Gilles A.Fleury, Aug 10 2008, Aug 24 2008; revised Oct 05 2008

Keywords

Comments

This sequence is a kind of optimized version of the sequence A060315 for which the inputs are the integers {0,1,...,n-1}. Here the inputs are optimized so that the smallest positive integer, that cannot be obtained, is maximized.
Further terms may be hard to find. Some additional terms (still to be proved) could be a(7)=2876, a(8)=24756, a(9)=346404. If anyone has found higher numbers please contact me.

Examples

			a(4)=18 because every integer can be calculated up to 17, using the optimal numbers {2,3,10}.
a(5)=70 because every integer can be calculated up to 69, using one of the two (!) optimal sequences {2,3,4,27} or {2,3,10,41}.
a(6)=406 because every integer can be calculated up to 405, using the optimal numbers {2,3,4,84,111}.

Crossrefs

Cf. A060315, A142153.

A142153 a(n) is the "highest smallest" positive integer that cannot be obtained from the (n-1) optimized integers (to be defined for each n) using each number at most once and the operators +, -, *, /.

Original entry on oeis.org

1, 2, 5, 18, 87, 451
Offset: 1

Views

Author

Gilles A.Fleury, Oct 05 2008

Keywords

Comments

This sequence is a kind of optimized version of the sequence A060315 for which the inputs are the integers {0,1,...,n-1}. Here the inputs are optimized so that the smallest positive integer, that cannot be obtained, is maximized.
Further terms may be hard to find. Some additional terms (still to be proved) could be a(7)=3495, a(8)=32355, a(9)=384289. If anyone has found higher numbers please contact me. - updated by Gilles A.Fleury, Jul 10 2017 and May 22 2018

Examples

			a(4) = 18 because every integer can be calculated up to 17, using one of the four (!) optimal sequences {2,3,10} or {2,3,14} or {2,6,11} or {2,6,13}.
a(5) = 87 because every integer can be calculated up to 86, using the optimal numbers {2,3,14,60}.
a(6) = 451 because every integer can be calculated up to 450, using the optimal numbers {2,3,4,63,152}. - _Gilles A.Fleury_, Mar 06 2009

Crossrefs

Cf. A141494, A060315.

Extensions

a(6) from Gilles A.Fleury, Mar 06 2009

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