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A275817
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Least positive integer s such that an integer square k^2 lies between s^2*n and s^2*(n+1), with s^2*n < k^2 < s^2*(n+1).
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3
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2, 3, 2, 4, 5, 3, 2, 3, 6, 7, 4, 3, 2, 3, 4, 8, 9, 5, 3, 5, 2, 3, 4, 5, 10, 11, 6, 4, 3, 5, 2, 5, 3, 4, 6, 12, 13, 7, 5, 4, 3, 7, 2, 5, 3, 4, 5, 7, 14, 15, 8, 5, 4, 3, 5, 7, 2, 5, 3, 7, 4, 6, 8, 16, 17, 9, 6, 5, 4, 3, 5, 7, 2, 5, 8, 3, 4, 5, 6, 9, 18, 19, 10, 7, 5, 4, 7, 3
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OFFSET
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0,1
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COMMENTS
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The corresponding values of k are provided in A275818.
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LINKS
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FORMULA
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If n = k^2 - 1 and k > 0, then a(n) = 2*k, A183162(n) = 1; otherwise a(n) = A183162(n).
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EXAMPLE
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a(0)=2, because 2^2*0 < 1^2 < 2^2*(0+1).
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MATHEMATICA
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Table[s = 1; While[Count[Range[n s^2 + 1, (n + 1) s^2 - 1], k_ /; IntegerQ@ Sqrt@ k] == 0, s++]; s, {n, 0, 120}] (* Michael De Vlieger, Aug 14 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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