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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 21 00:36 EDT 2022. Contains 353886 sequences. (Running on oeis4.)