

A072689


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


2



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
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OFFSET

1,2


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


FORMULA

a(n) = A057427(n  A048760(n)) * (A000196(A048760(n))*2 + 1).
a(n) = A048761(n)  A048760(n).


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 *)


CROSSREFS

Cf. A000196, A000290, A048760, A048761, A072690.
Sequence in context: A128046 A102899 A353327 * A021972 A193451 A335809
Adjacent sequences: A072686 A072687 A072688 * A072690 A072691 A072692


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Jul 02 2002


STATUS

approved



