A275817 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).

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

Offset: 0

Author

Hugo Pfoertner, Aug 09 2016

Keywords

• nonn

Comments

The corresponding values of k are provided in A275818.

Examples

			a(0)=2, because 2^2*0 < 1^2 < 2^2*(0+1).
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 0..1000
• Michael Weiss, On the Distribution of Rational Squares, arXiv:1510.07362 [math.NT], 2015.
• Michael Weiss, Where Are the Rational Squares?, The American Mathematical Monthly, Vol. 124, No. 3 (March 2017), pp. 255-259.

Crossrefs

Cf. A183162, A275818.

Programs

Mathematica

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 *)

Formula

If n = k^2 - 1 and k > 0, then a(n) = 2*k, A183162(n) = 1; otherwise a(n) = A183162(n).