A080883 - OEIS

%I #20 Sep 22 2025 16:00:41

%S 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,

%T 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,

%U 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

%N Distance of n to next square.

%C The following sequences all have the same parity: A004737, A006590, A027052, A071028, A071797, A078358, A078446, A080883. - _Jeremy Gardiner_, Dec 30 2006

%H G. C. Greubel, <a href="/A080883/b080883.txt">Table of n, a(n) for n = 0..1000</a>

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

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

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

%o (PARI) a(n) = (sqrtint(n)+1)^2-n; \\ _Michel Marcus_, May 22 2024

%o (Magma) [Floor(1+Sqrt(n))^2 -n: n in [0..90]]; // _G. C. Greubel_, Nov 07 2019

%o (SageMath) [floor(1+sqrt(n))^2 -n for n in (0..90)] # _G. C. Greubel_, Nov 07 2019

%o (GAP) List([0..90], n-> Int(1+RootInt(n))^2 -n); # _G. C. Greubel_, Nov 07 2019

%Y Cf. A075555.

%Y Cf. A066635, A053188. - _R. J. Mathar_, Aug 08 2009

%K nonn,easy

%O 0,2

%A _Ralf Stephan_, Mar 29 2003