Revision History for A134361
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
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#10 by Charles R Greathouse IV at Fri Jul 09 12:10:34 EDT 2021
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#9 by Charles R Greathouse IV at Fri Jul 09 12:10:23 EDT 2021
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| COMMENTS
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Can be used, for example, to derive A084788 and A084790 from A084789. - Charles R Greathouse IV, Jul 09 2021
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| PROG
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(PARI) a(n)=my(v=List()); for(i=0, logint(n, 3)+1, my(t=3^i); t<<=if(t>n, 0, exponent(n\t)+1); listput(v, t)); Set(v)[1] \\ Charles R Greathouse IV, Jul 09 2021
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| KEYWORD
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nonn,easy
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| STATUS
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approved
editing
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#8 by Charles R Greathouse IV at Thu Nov 21 12:49:08 EST 2013
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| MATHEMATICA
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With[{pf23=Union[Flatten[Table[Times@@@Tuples[{2, 3}, n], {n, 0, 6}]]]}, Flatten[Table[Select[pf23, #>=n&, 1], {n, 80}]]] (* From }]]] (* _Harvey P. Dale, _, Mar 07 2012 *)
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Discussion
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| Thu Nov 21
| 12:49
| OEIS Server: https://oeis.org/edit/global/2062
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#7 by Russ Cox at Fri Mar 30 16:50:46 EDT 2012
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| AUTHOR
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_N. J. A. Sloane (njas(AT)research.att.com), _, Aug 23 2009; corrected Mar 07 2012
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Discussion
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| Fri Mar 30
| 16:50
| OEIS Server: https://oeis.org/edit/global/110
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#6 by Harvey P. Dale at Wed Mar 07 14:29:27 EST 2012
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#5 by Harvey P. Dale at Wed Mar 07 14:29:23 EST 2012
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| MATHEMATICA
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With[{pf23=Union[Flatten[Table[Times@@@Tuples[{2, 3}, n], {n, 0, 6}]]]}, Flatten[Table[Select[pf23, #>=n&, 1], {n, 80}]]] (* From Harvey P. Dale, Mar 07 2012 *)
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| STATUS
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approved
editing
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#4 by N. J. A. Sloane at Wed Mar 07 12:50:05 EST 2012
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#3 by N. J. A. Sloane at Wed Mar 07 12:50:00 EST 2012
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| DATA
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1, 32, 3, 54, 56, 96, 98, 98, 9, 1512, 1512, 1512, 1516, 1516, 1516, 2516, 2518, 2518, 2524, 2524, 2524, 2524, 2524, 2524, 2527, 27, 27, 32, 32, 32, 4532, 4532, 4536, 4536, 4536, 4536, 4548, 4548, 4548, 4548, 4548, 4548, 4548, 4548, 4548, 4548, 4548, 4548, 7554, 7554, 7554, 7554, 7554, 7554, 7564, 7564, 7564, 7564, 7564, 7564, 7564, 7564, 7564, 7564, 7572, 7572, 7572, 7572, 7572, 7572, 7572, 7572
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| AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2009; corrected Mar 07 2012
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| STATUS
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approved
editing
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#2 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010
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| NAME
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Cardinality of the largesta(n) = smallest criticalinteger >= n setwhich inhas anyonly Latinprime squarefactors of2 orderand n3.
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| DATA
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0, 1, 3, 3, 5, 5, 9, 9, 9, 9, 15, 15, 15, 15, 15, 15, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 27, 27, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 775, 1175, 1875
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| OFFSET
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1,32
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| COMMENTS
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A critical set in an n x n array is a set C of given entries,
such that there exists a unique extension of C to an n x n Latin
square and no proper subset of C has this property.
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| LINKS
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H. Hatami and E. S. Mahmoodian, <a href="http://arXiv.org/abs/math/0701014">A lower bound for the size of the largest critical sets in Latin squares</a>
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| PROG
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(R) f <- function(n) nextn(n, factors = c(2, 3))
a <- matrix(1:256, ncol=1)
apply(a, 1, f)
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| CROSSREFS
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Cf. A130916, A134361, A151969.
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| KEYWORD
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nonn,hard,new
nonn
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| AUTHOR
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Ralf Stephan, Jan 16 2008
N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2009
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#1 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008
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| NAME
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Cardinality of the largest critical set in any Latin square of order n.
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| DATA
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0, 1, 3, 7, 11, 18
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| OFFSET
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1,3
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| COMMENTS
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A critical set in an n x n array is a set C of given entries,
such that there exists a unique extension of C to an n x n Latin
square and no proper subset of C has this property.
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| LINKS
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H. Hatami and E. S. Mahmoodian, <a href="http://arXiv.org/abs/math/0701014">A lower bound for the size of the largest critical sets in Latin squares</a>
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| KEYWORD
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nonn,hard
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| AUTHOR
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Ralf Stephan, Jan 16 2008
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| STATUS
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approved
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