A080883 Distance of n to next square.

1, 3, 2, 1, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 18, 17, 16, 15, 14, 13

Offset

0,2

Comments

The following sequences all have the same parity: A004737, A006590, A027052, A071028, A071797, A078358, A078446, A080883. - Jeremy Gardiner, Dec 30 2006

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = floor( sqrt(n)+1 )^2 - n.

Maple

A080883 := proc(n) (floor(sqrt(n)+1))^2 -n ; end: seq( A080883(n), n=0..40) ; # R. J. Mathar, Aug 08 2009

Mathematica

Table[Floor[1+Sqrt[n]]^2 -n, {n, 0, 90}] (* G. C. Greubel, Nov 07 2019 *)

Prog

(PARI) a(n) = (sqrtint(n)+1)^2-n; \\ Michel Marcus, May 22 2024
(Magma) [Floor(1+Sqrt(n))^2 -n: n in [0..90]]; // G. C. Greubel, Nov 07 2019
(Sage) [floor(1+sqrt(n))^2 -n for n in (0..90)] # G. C. Greubel, Nov 07 2019
(GAP) List([0..90], n-> Int(1+RootInt(n))^2 -n); # G. C. Greubel, Nov 07 2019

Crossrefs

Cf. A075555.

Cf. A066635, A053188. - R. J. Mathar, Aug 08 2009

Sequence in context: A309219 A019587 A102427 * A021315 A337315 A068389

Adjacent sequences: A080880 A080881 A080882 * A080884 A080885 A080886

Keyword

nonn,easy

Author

Ralf Stephan, Mar 29 2003

Status

approved