A053188 Distance from n to nearest square.

0, 0, 1, 1, 0, 1, 2, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4

Offset

0,7

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to distance to nearest element of some set

Formula

a(n) = |floor(sqrt(n) + 1/2)^2 - n|. - Ridouane Oudra, May 01 2019

a(n) <= sqrt(n). - Charles R Greathouse IV, Nov 16 2022

Example

a(7)=2 since 9 is the closest square to 7 and |9-7| = 2.

Mathematica

Flatten[Table[Abs[Nearest[Range[0, 25]^2, n]-n], {n, 0, 120}]]  (* Harvey P. Dale, Mar 14 2011 *)

Prog

(Haskell)
a053188 0 = 0
a053188 n = min (n - last xs) (head ys - n) where
   (xs, ys) = span (< n) a000290_list
-- Reinhard Zumkeller, Nov 28 2011
(Python)
from math import isqrt
def A053188(n): return abs(((m:=isqrt(n))+int(n-m*(m+1)>=1))**2-n) # Chai Wah Wu, Aug 03 2022
(PARI) a(n)=abs(((sqrtint(4*n) + 1)\2)^2 - n) \\ Charles R Greathouse IV, Nov 16 2022

Crossrefs

Cf. A053187, A074989, A000290.

Sequence in context: A368494 A061926 A180835 * A109389 A098884 A297964

Adjacent sequences: A053185 A053186 A053187 * A053189 A053190 A053191

Keyword

easy,nonn

Author

Henry Bottomley, Mar 01 2000

Status

approved