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A054040
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a(n) terms of series {1/sqrt(j)} are >= n.
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3
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1, 3, 5, 7, 10, 14, 18, 22, 27, 33, 39, 45, 52, 60, 68, 76, 85, 95, 105, 115, 126, 138, 150, 162, 175, 189, 202, 217, 232, 247, 263, 280, 297, 314, 332, 351, 370, 389, 409, 430, 451, 472, 494, 517, 540, 563, 587, 612, 637, 662, 688, 715, 741, 769, 797, 825
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| For the most part the first differences have the form {2k, 2k, 2k, 2k+1} (A004524). Therefore for the most part the second differences are {0, 0, 1, 1}. See A082915 for the exceptions. - Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 18 2003
a(100)=2574, a(1000)=250731 & a(10000)=25007302 which differs from Sum{i=4..104}A004524(i)=2625, Sum{i=4..1004}A004524(i)=251250 & Sum{i=4..10004}A004524(i)=25012500. - Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 18 2003
A054040(n) <= A011848(n+2), A054040(10000)=25007302 and A011848(n+2)=25007500. - Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 18 2003
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EXAMPLE
| Let b(k) = 1 + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(k):
.k.......1....2.....3.....4.....5.....6.....7
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b(k)...1.00..1.71..2.28..2.78..3.23..3.64..4.01
For A019529 we have:
n=0: smallest k is a(0) = 1 since 1.00 > 0
n=1: smallest k is a(1) = 2 since 1.71 > 1
n=2: smallest k is a(2) = 3 since 2.28 > 2
n=3: smallest k is a(3) = 5 since 3.23 > 3
n=4: smallest k is a(4) = 7 since 4.01 > 4
For AA054040 we have:
n=1: smallest k is a(1) = 1 since 1.00 >= 1
n=2: smallest k is a(2) = 3 since 2.28 >= 2
n=3: smallest k is a(3) = 5 since 3.23 >= 3
n=4: smallest k is a(4) = 7 since 4.01 >= 4
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MATHEMATICA
| f[n_] := Block[{k = 0, s = 0}, While[s < n, k++; s = N[s + 1/Sqrt[k], 50]]; k]; Table[f[n], {n, 1, 60}]
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CROSSREFS
| Cf. A002387, A004080, A082915, A054044, A011848, A082915.
See A019529 for a different version.
Sequence in context: A173137 A194170 A194166 * A011848 A131673 A151945
Adjacent sequences: A054037 A054038 A054039 * A054041 A054042 A054043
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KEYWORD
| nonn
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AUTHOR
| Asher Auel (asher.auel(AT)reed.edu) Apr 13 2000
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EXTENSIONS
| Definition and offset modified by N. J. A. Sloane, Sep 01 2009
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