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Search: id:A138813
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| A138813 |
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a(0) = 1; thereafter a(n) = sum{k=0 to n-1} ceiling(n/a(k)). |
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2
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| 1, 1, 4, 7, 10, 14, 17, 20, 24, 28, 31, 35, 38, 42, 45, 50, 53, 57, 61, 64, 67, 73, 77, 80, 83, 88, 91, 94, 97, 104, 107, 111, 115, 119, 122, 126, 131, 135, 138, 142, 145, 151, 154, 160, 163, 167, 171, 174, 177, 182, 186, 191, 195, 199, 203, 206, 209, 216, 220, 223
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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Probably a(n) ~ sqrt(2) n ln(n)^(1/2) as n -> oo. - Robert Israel (israel(AT)math.ubc.ca), May 02 2008
Comment from Andrew V. Sutherland (drew(AT)math.mit.edu), May 02 2008 (Start): This is supported by the following data:
a( 2)= 4, a(n)/n=2.0000, a(n)/(n*sqrt(ln(n)))=2.4022
a( 4)= 10, a(n)/n=2.5000, a(n)/(n*sqrt(ln(n)))=2.1233
a( 8)= 24, a(n)/n=3.0000, a(n)/(n*sqrt(ln(n)))=2.0804
a( 16)= 53, a(n)/n=3.3125, a(n)/(n*sqrt(ln(n)))=1.9894
a( 32)= 115, a(n)/n=3.5938, a(n)/(n*sqrt(ln(n)))=1.9304
a( 64)= 244, a(n)/n=3.8125, a(n)/(n*sqrt(ln(n)))=1.8695
a( 128)= 514, a(n)/n=4.0156, a(n)/(n*sqrt(ln(n)))=1.8230
a( 256)= 1075, a(n)/n=4.1992, a(n)/(n*sqrt(ln(n)))=1.7832
a( 512)= 2237, a(n)/n=4.3691, a(n)/(n*sqrt(ln(n)))=1.7493
a( 1024)= 4642, a(n)/n=4.5332, a(n)/(n*sqrt(ln(n)))=1.7218
a( 2048)= 9608, a(n)/n=4.6914, a(n)/(n*sqrt(ln(n)))=1.6990
a( 4096)= 19843, a(n)/n=4.8445, a(n)/(n*sqrt(ln(n)))=1.6797
a( 8192)= 40895, a(n)/n=4.9921, a(n)/(n*sqrt(ln(n)))=1.6630
a( 16384)= 84129, a(n)/n=5.1348, a(n)/(n*sqrt(ln(n)))=1.6483
a( 32768)= 172797, a(n)/n=5.2733, a(n)/(n*sqrt(ln(n)))=1.6354
a( 65536)= 354437, a(n)/n=5.4083, a(n)/(n*sqrt(ln(n)))=1.6240
a(131072)= 726143, a(n)/n=5.5400, a(n)/(n*sqrt(ln(n)))=1.6139 (End)
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MATHEMATICA
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a = {1}; Do[AppendTo[a, Sum[Ceiling[n/a[[k]]], {k, 1, n}]], {n, 1, 70}]; a - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 04 2008
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CROSSREFS
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Cf. A138812.
Sequence in context: A080600 A067497 A123384 this_sequence A161187 A133497 A064368
Adjacent sequences: A138810 A138811 A138812 this_sequence A138814 A138815 A138816
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Mar 31 2008
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 04 2008
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