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

Author

Ralf Stephan, Mar 29 2003

Keywords

• nonn
• easy

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

Crossrefs

Cf. A075555.

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

Programs

GAP

List([0..90], n-> Int(1+RootInt(n))^2 -n); # G. C. Greubel, Nov 07 2019

Magma

[Floor(1+Sqrt(n))^2 -n: n in [0..90]]; // G. C. Greubel, Nov 07 2019

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 *)

PARI

a(n) = (sqrtint(n)+1)^2-n; \\ Michel Marcus, May 22 2024

Sage

[floor(1+sqrt(n))^2 -n for n in (0..90)] # G. C. Greubel, Nov 07 2019

Formula

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