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Search: id:A093005
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| A093005 |
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The lone multiple of n among the next n numbers. |
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+0
7
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| 1, 2, 6, 8, 15, 18, 28, 32, 45, 50, 66, 72, 91, 98, 120, 128, 153, 162, 190, 200, 231, 242, 276, 288, 325, 338, 378, 392, 435, 450, 496, 512, 561, 578, 630, 648, 703, 722, 780, 800, 861, 882, 946, 968, 1035, 1058, 1128, 1152, 1225, 1250, 1326, 1352, 1431, 1458
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Consider the triangle
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
... Then sequence contains the multiple of n in the n-th row.
Interleaves A000384 and A001105. - Paul Barry (pbarry(AT)wit.ie), Jun 29 2006
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FORMULA
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a(2n-1)= n*(2n-1), a(2n) = 2n^2.
G.f.: x(1+x+2x^2)/((1+x)^2*(1-x)^3); a(n)=a(n-1)+2a(n-2)-2a(n-3)-a(n-4)+a(n-5); a(n)=n(2n+1)/4-n(-1)^n/4; - Paul Barry (pbarry(AT)wit.ie), Jun 29 2006
a(n)= n*(floor((n+1)/2) - Olivier GERARD (olivier.gerard(AT)gmail.com), Jun 21 2007
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MAPLE
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a:=n->add(add(1-(-1)^j, j=1..n), j=1..n):seq(a(n)/2, n=1..52); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 13 2008]
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MATHEMATICA
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a[ n_Integer ] := n Floor[(n + 1)/2] - Olivier GERARD (olivier.gerard(AT)gmail.com), Jun 21 2007
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CROSSREFS
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Cf. A008619 ( a(n)/n ).
Sequence in context: A135619 A029933 A128913 this_sequence A049818 A066189 A137848
Adjacent sequences: A093002 A093003 A093004 this_sequence A093006 A093007 A093008
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 29 2004
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EXTENSIONS
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Corrected and extended by Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 08 2006
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