A174806 a(n) = n-floor(sqrt(n))^2-floor(sqrt(n-floor(sqrt(n))^2))^2; difference between n and sum of two largest distinct squares <= n.

0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 3, 4, 0, 0, 1, 2, 0, 1, 2, 3, 4, 0, 1, 0, 0, 1, 2, 0, 1, 2, 3, 4, 0, 1, 2, 3, 0, 0, 1, 2, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 0, 1, 2, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 6, 0, 0, 0, 1, 2, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 0, 0, 1, 2, 0

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Mar 29 2010

Keywords

• nonn

Comments

If a(n)=0 then n is a sum of two squares A001481, but not conversely. For the sum of two squares n = 18, 32, 41, ... we have a(n) > 0. - Thomas Ordowski, Jul 11 2014

Examples

			24=4^2+8;8-2^2=4, 115=10^2+15;15-3^2=6,..
		

Links

• Michel Marcus, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001481, A053186, A053610.

Programs

Mathematica

a[n_]:=n-Floor[Sqrt[n]]^2-Floor[Sqrt[n-Floor[Sqrt[n]]^2]]^2;
Table[a[n], {n,0,6!}]

PARI

a(n) = my(x=sqrtint(n)^2); n - x - sqrtint((n-x))^2; \\ Michel Marcus, Dec 17 2022

Formula

a(n) = 0 iff A053610(n) < 3 and 0 < a(n) = m^2 iff A053610(n) = 3. - Thomas Ordowski, Jul 12 2014