

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).


3



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

0,1


COMMENTS

The corresponding values of k are provided in A275818.


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. 255259.


FORMULA

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


EXAMPLE

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


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 *)


CROSSREFS

Cf. A183162, A275818.
Sequence in context: A304742 A003976 A252371 * A286533 A172520 A290094
Adjacent sequences: A275814 A275815 A275816 * A275818 A275819 A275820


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Aug 09 2016


STATUS

approved



