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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.
2
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
0,8
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
LINKS
FORMULA
a(n) = 0 iff A053610(n) < 3 and 0 < a(n) = m^2 iff A053610(n) = 3. - Thomas Ordowski, Jul 12 2014
EXAMPLE
24=4^2+8;8-2^2=4, 115=10^2+15;15-3^2=6,..
MATHEMATICA
a[n_]:=n-Floor[Sqrt[n]]^2-Floor[Sqrt[n-Floor[Sqrt[n]]^2]]^2;
Table[a[n], {n, 0, 6!}]
PROG
(PARI) a(n) = my(x=sqrtint(n)^2); n - x - sqrtint((n-x))^2; \\ Michel Marcus, Dec 17 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved