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A183162
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Least integer k such that Floor(k*sqrt(n+1))>k*sqrt(n).
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5
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3, 2, 1, 5, 3, 2, 3, 1, 7, 4, 3, 2, 3, 4, 1, 9, 5, 3, 5, 2, 3, 4, 5, 1, 11, 6, 4, 3, 5, 2, 5, 3, 4, 6, 1, 13, 7, 5, 4, 3, 7, 2, 5, 3, 4, 5, 7, 1, 15, 8, 5, 4, 3, 5, 7, 2, 5, 3, 7, 4, 6, 8, 1, 17, 9, 6, 5, 4, 3, 5, 7, 2, 5, 8, 3, 4, 5, 6, 9, 1, 19, 10, 7, 5, 4, 7, 3, 5, 9
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OFFSET
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1,1
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COMMENTS
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The above definition is equivalent to this: least
positive integer k such that one of the following holds:
(1) there is an integer J such that
n*k^2 < J^2 < (n+1)*k^2; or
(2) there is an integer J such that (n+1)*k^2 = J^2.
Note that (1) is equivalent to the existence of a rational
number H with denominator k such that
n < H^2 < n+1.
Positions of 1: A005563.
Positions of 2: 2*A000217.
Positions of 2n+1: A000290.
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LINKS
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Table of n, a(n) for n=1..89.
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EXAMPLE
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The results are easily read from an array of k*sqrt(n),
represented here by approximations:
1.00 1.41 1.73 2.00 2.24 2.45 2.65
2.00 2.83 3.46 4.00 4.47 4.90 5.29
3.00 4.24 5.20 6.00 6.71 7.35 7.94
4.00 5.66 6.93 8.00 8.94 9.80 10.58
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CROSSREFS
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Cf. A183163, A183164, A005563, A000217, A000290.
Sequence in context: A030313 A171746 A113977 * A019587 A102427 A080883
Adjacent sequences: A183159 A183160 A183161 * A183163 A183164 A183165
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Dec 27 2010
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STATUS
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approved
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