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A053188
Distance from n to nearest square.
20
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
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
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Mar 01 2000
STATUS
approved