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%I #24 Oct 07 2017 03:38:42
%S 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,
%T 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,
%U 17,9,6,5,4,3,5,7,2,5,8,3,4,5,6,9,18,19,10,7,5,4,7,3
%N 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).
%C The corresponding values of k are provided in A275818.
%H Hugo Pfoertner, <a href="/A275817/b275817.txt">Table of n, a(n) for n = 0..1000</a>
%H Michael Weiss, <a href="http://arxiv.org/abs/1510.07362">On the Distribution of Rational Squares</a>, arXiv:1510.07362 [math.NT], 2015.
%H Michael Weiss, <a href="https://dx.doi.org/10.4169/amer.math.monthly.124.3.255">Where Are the Rational Squares?</a>, The American Mathematical Monthly, Vol. 124, No. 3 (March 2017), pp. 255-259.
%F If n = k^2 - 1 and k > 0, then a(n) = 2*k, A183162(n) = 1; otherwise a(n) = A183162(n).
%e a(0)=2, because 2^2*0 < 1^2 < 2^2*(0+1).
%t 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 *)
%Y Cf. A183162, A275818.
%K nonn
%O 0,1
%A _Hugo Pfoertner_, Aug 09 2016
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