A072689 Difference between (least square >= n) and (largest square <= n).

0, 3, 3, 0, 5, 5, 5, 5, 0, 7, 7, 7, 7, 7, 7, 0, 9, 9, 9, 9, 9, 9, 9, 9, 0, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 0, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17

Offset: 1

Author

Reinhard Zumkeller, Jul 02 2002

Keywords

• nonn

Comments

a(n) = 0 iff n is a square.

a(n) = 1+2*A000196(n) if n is not a square. - Robert Israel, Sep 22 2020

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000196, A000290, A048760, A048761, A072690.

Programs

Maple

f:= proc(n) local t; t:= floor(sqrt(n));
  if n = t^2 then 0 else 1 + 2*t fi
end proc:
map(f, [$1..100]); # Robert Israel, Sep 22 2020

Mathematica

ds[n_]:=Module[{s=Sqrt[n]},If[IntegerQ[s],0,1+2Floor[s]]]; Array[ds,80] (* Harvey P. Dale, Dec 05 2013 *)

Formula

a(n) = A057427(n - A048760(n)) * (A000196(A048760(n))*2 + 1).

a(n) = A048761(n) - A048760(n).