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Search: id:A127264
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| A127264 |
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Nearest integer to 2*Sum[1/i,{i,1,10^n/2}] - 1. |
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+0
1
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| 4, 8, 13, 17, 22, 26, 31, 36, 40, 45, 49, 54, 59, 63, 68, 72, 77, 82, 86, 91, 95, 100, 105, 109, 114, 119, 123, 128, 132, 137, 142, 146, 151, 155, 160, 165, 169, 174, 178, 183, 188, 192, 197, 201, 206, 211, 215, 220, 224, 229, 234, 238, 243, 247, 252, 257, 261, 266, 270, 275
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The original definition was: Nearest integer to Sum[(10^n-i)/i,{i,1,10^n/2}]/(10^n/2), but this was simplified to the present definition by Jon Schoenfield, Aug 05 2008
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LINKS
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Jon Schoenfield, Table of n, a(n) for n = 1..1000
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FORMULA
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a(n) = round(2 * (ln(m) + Gamma) + 1/m - ...) - 1 where m = 10^n / 2 and Gamma = 0.57721566490153286... (the Euler-Mascheroni constant A001620). - Jon Schoenfield, Aug 05 2008
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EXAMPLE
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a(1)=4 because round((9/1 + 8/2 + 7/3 + 6/4 + 5/5)/5) is 4.
a(2)=8 because round((99/1 + 98/2 +... +50/50))/50 is 8.
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MAPLE
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for i from 10 to 11 by 2 do s:=0; t:=0; for d from i/2 to i -1 do s:= s + (d / (i - d)); t:= t +1; end do; print(round((s / t))); end do;
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CROSSREFS
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Different from A004081, although the sequences have the same first few terms.
Sequence in context: A081843 A004938 A004081 this_sequence A130236 A034856 A064609
Adjacent sequences: A127261 A127262 A127263 this_sequence A127265 A127266 A127267
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KEYWORD
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nonn
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AUTHOR
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Ben Thurston (benthurston27(AT)yahoo.com), Mar 27 2007
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EXTENSIONS
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Extended and edited by John W. Layman (layman(AT)math.vt.edu), Jul 10 2007
Terms from a(11) onwards from Jon Schoenfield, Aug 05 2008
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