A068527 Difference between smallest square >= n and n.

0, 0, 2, 1, 0, 4, 3, 2, 1, 0, 6, 5, 4, 3, 2, 1, 0, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9

Offset

0,3

Comments

The greedy inverse (sequence of the smallest k such that a(k)=n) starts 0, 3, 2, 6, 5, 11, 10, 18, 17, 27, 26, 38, 37, 51, 50, ... and appears to be given by A010000 and A002522, interleaved. - R. J. Mathar, Nov 17 2014

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Formula

a(n) = A048761(n) - n = ceiling(sqrt(n))^2 - n.

G.f.: (-x^2 + (x-x^2)*Sum_{m>=1} (1+2*m)*x^(m^2))/(1-x)^2. This sum is related to Jacobi Theta functions. - Robert Israel, Nov 17 2014

Maple

A068527:=n->ceil(sqrt(n))^2-n; seq(A068527(n), n=0..100); # Wesley Ivan Hurt, Jun 11 2014

Mathematica

Table[Ceiling[Sqrt[n]]^2-n, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2012 *)

Prog

(Magma) [ Ceiling(Sqrt(n))^2-n : n in [0..50] ]; // Wesley Ivan Hurt, Jun 11 2014
(PARI) a(n)=if(issquare(n), 0, (sqrtint(n)+1)^2-n) \\ Charles R Greathouse IV, Oct 22 2014
(Python)
from math import isqrt
def A068527(n): return 0 if n == 0 else (isqrt(n-1)+1)**2-n # Chai Wah Wu, Feb 22 2022

Crossrefs

Cf. A053186, A068869, A066857.

Bisections: A348596, A350962.

Sequence in context: A334122 A086802 A092488 * A361989 A218599 A051623

Adjacent sequences: A068524 A068525 A068526 * A068528 A068529 A068530

Keyword

nonn,easy

Author

Vladeta Jovovic, Mar 21 2002

Status

approved