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A174806
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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.
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2
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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
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OFFSET
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0,8
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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24=4^2+8;8-2^2=4, 115=10^2+15;15-3^2=6,..
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MATHEMATICA
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a[n_]:=n-Floor[Sqrt[n]]^2-Floor[Sqrt[n-Floor[Sqrt[n]]^2]]^2;
Table[a[n], {n, 0, 6!}]
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PROG
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(PARI) a(n) = my(x=sqrtint(n)^2); n - x - sqrtint((n-x))^2; \\ Michel Marcus, Dec 17 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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