cp's OEIS Frontend

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

%I A072689 #13 Sep 23 2020 03:27:26
%S A072689 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,
%T A072689 11,11,11,11,0,13,13,13,13,13,13,13,13,13,13,13,13,0,15,15,15,15,15,
%U A072689 15,15,15,15,15,15,15,15,15,0,17,17,17,17,17,17,17,17,17,17,17,17,17,17
%N A072689 Difference between (least square >= n) and (largest square <= n).
%C A072689 a(n) = 0 iff n is a square.
%C A072689 a(n) = 1+2*A000196(n) if n is not a square. - _Robert Israel_, Sep 22 2020
%H A072689 Robert Israel, <a href="/A072689/b072689.txt">Table of n, a(n) for n = 1..10000</a>
%F A072689 a(n) = A057427(n - A048760(n)) * (A000196(A048760(n))*2 + 1).
%F A072689 a(n) = A048761(n) - A048760(n).
%p A072689 f:= proc(n) local t; t:= floor(sqrt(n));
%p A072689   if n = t^2 then 0 else 1 + 2*t fi
%p A072689 end proc:
%p A072689 map(f, [$1..100]); # _Robert Israel_, Sep 22 2020
%t A072689 ds[n_]:=Module[{s=Sqrt[n]},If[IntegerQ[s],0,1+2Floor[s]]]; Array[ds,80] (* _Harvey P. Dale_, Dec 05 2013 *)
%Y A072689 Cf. A000196, A000290, A048760, A048761, A072690.
%K A072689 nonn
%O A072689 1,2
%A A072689 _Reinhard Zumkeller_, Jul 02 2002